Transformation Groups In Differential Geometry

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Transformation Groups in Differential Geometry

Author : Shoshichi Kobayashi
Publisher : Springer Science & Business Media
ISBN 13 : 3642619819
Total Pages : 192 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis Transformation Groups in Differential Geometry by : Shoshichi Kobayashi

Download or read book Transformation Groups in Differential Geometry written by Shoshichi Kobayashi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Given a mathematical structure, one of the basic associated mathematical objects is its automorphism group. The object of this book is to give a biased account of automorphism groups of differential geometric struc tures. All geometric structures are not created equal; some are creations of ~ods while others are products of lesser human minds. Amongst the former, Riemannian and complex structures stand out for their beauty and wealth. A major portion of this book is therefore devoted to these two structures. Chapter I describes a general theory of automorphisms of geometric structures with emphasis on the question of when the automorphism group can be given a Lie group structure. Basic theorems in this regard are presented in §§ 3, 4 and 5. The concept of G-structure or that of pseudo-group structure enables us to treat most of the interesting geo metric structures in a unified manner. In § 8, we sketch the relationship between the two concepts. Chapter I is so arranged that the reader who is primarily interested in Riemannian, complex, conformal and projective structures can skip §§ 5, 6, 7 and 8. This chapter is partly based on lec tures I gave in Tokyo and Berkeley in 1965.

Modern Geometry - Methods and Applications

Author : B.A. Dubrovin
Publisher : Springer
ISBN 13 : 9780387908724
Total Pages : 464 pages
Book Rating : 4.9/5 (87 download)

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Book Synopsis Modern Geometry - Methods and Applications by : B.A. Dubrovin

Download or read book Modern Geometry - Methods and Applications written by B.A. Dubrovin and published by Springer. This book was released on 1984-03-16 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: manifolds, transformation groups, and Lie algebras, as well as the basic concepts of visual topology. It was also agreed that the course should be given in as simple and concrete a language as possible, and that wherever practic able the terminology should be that used by physicists. Thus it was along these lines that the archetypal course was taught. It was given more permanent form as duplicated lecture notes published under the auspices of Moscow State University as: Differential Geometry, Parts I and II, by S. P. Novikov, Division of Mechanics, Moscow State University, 1972. Subsequently various parts of the course were altered, and new topics added. This supplementary material was published (also in duplicated form) as Differential Geometry, Part III, by S. P. Novikov and A. T. Fomenko, Division of Mechanics, Moscow State University, 1974. The present book is the outcome of a reworking, re-ordering, and ex tensive elaboration of the above-mentioned lecture notes. It is the authors' view that it will serve as a basic text from which the essentials for a course in modern geometry may be easily extracted. To S. P. Novikov are due the original conception and the overall plan of the book. The work of organizing the material contained in the duplicated lecture notes in accordance with this plan was carried out by B. A. Dubrovin.

Theory of Transformation Groups I

Author : Sophus Lie
Publisher : Springer
ISBN 13 : 3662462117
Total Pages : 643 pages
Book Rating : 4.6/5 (624 download)

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Book Synopsis Theory of Transformation Groups I by : Sophus Lie

Download or read book Theory of Transformation Groups I written by Sophus Lie and published by Springer. This book was released on 2015-03-12 with total page 643 pages. Available in PDF, EPUB and Kindle. Book excerpt: This modern translation of Sophus Lie's and Friedrich Engel's “Theorie der Transformationsgruppen I” will allow readers to discover the striking conceptual clarity and remarkably systematic organizational thought of the original German text. Volume I presents a comprehensive introduction to the theory and is mainly directed towards the generalization of ideas drawn from the study of examples. The major part of the present volume offers an extremely clear translation of the lucid original. The first four chapters provide not only a translation, but also a contemporary approach, which will help present day readers to familiarize themselves with the concepts at the heart of the subject. The editor's main objective was to encourage a renewed interest in the detailed classification of Lie algebras in dimensions 1, 2 and 3, and to offer access to Sophus Lie's monumental Galois theory of continuous transformation groups, established at the end of the 19th Century. Lie groups are widespread in mathematics, playing a role in representation theory, algebraic geometry, Galois theory, the theory of partial differential equations and also in physics, for example in general relativity. This volume is of interest to researchers in Lie theory and exterior differential systems and also to historians of mathematics. The prerequisites are a basic knowledge of differential calculus, ordinary differential equations and differential geometry.

Proceedings of the Conference on Transformation Groups

Author : P. S. Mostert
Publisher : Springer Science & Business Media
ISBN 13 : 3642461417
Total Pages : 470 pages
Book Rating : 4.6/5 (424 download)

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Book Synopsis Proceedings of the Conference on Transformation Groups by : P. S. Mostert

Download or read book Proceedings of the Conference on Transformation Groups written by P. S. Mostert and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: These Proceedings contain articles based on the lectures and in formal discussions at the Conference on Transformation Groups held at Tulane University, May 8 to June 2, 1967 under the sponsorship of the Advanced Science Seminar Projects of the National Science Foun dation (Contract No. GZ 400). They differ, however, from many such Conference proceedings in that particular emphasis has been given to the review and exposition of the state of the theory in its various mani festations, and the suggestion of direction to further research, rather than purely on the publication of research papers. That is not to say that there is no new material contained herein. On the contrary, there is an abundance of new material, many new ideas, new questions, and new conjectures~arefully incorporated within the framework of the theory as the various authors see it. An original objective of the Conference and of this report was to supply a much needed review of and supplement to the theory since the publication of the three standard works, MONTGOMERY and ZIPPIN, Topological Transformation Groups, Interscience Pub lishers, 1955, BOREL et aI. , Seminar on Transformation Groups, Annals of Math. Surveys, 1960, and CONNER and FLOYD, Differen tial Periodic Maps, Springer-Verlag, 1964. Considering this objective ambitious enough, it was decided to limit the survey to that part of Transformation Group Theory derived from the Montgomery School.

Transformation Groups for Beginners

Author : Sergeĭ Vasilʹevich Duzhin
Publisher : American Mathematical Soc.
ISBN 13 : 0821836439
Total Pages : 246 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Transformation Groups for Beginners by : Sergeĭ Vasilʹevich Duzhin

Download or read book Transformation Groups for Beginners written by Sergeĭ Vasilʹevich Duzhin and published by American Mathematical Soc.. This book was released on 2004 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for undergraduate students and all those interested in mathematics. Its goal is to give an easy introduction to the concept of a transformation group using examples from different areas of mathematics. The warm-up of the first two chapters includes a discussion of algebraic operations on points in the plane, and of Euclidean plane movements. Then the notions of a transformation group and of an abstract group are introduced. Group actions, orbits, and invariants constitute the subject of the next chapter. The book concludes with an elementary exposition of the basic ideas of Sophus Lie about symmetries of differential equations. The book contains plenty of figures, as well as many exercises with hints and solutions, which help the reader to master the material.

Differential Geometry

Author : Heinrich W. Guggenheimer
Publisher : Courier Corporation
ISBN 13 : 0486157202
Total Pages : 400 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Differential Geometry by : Heinrich W. Guggenheimer

Download or read book Differential Geometry written by Heinrich W. Guggenheimer and published by Courier Corporation. This book was released on 2012-04-27 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text contains an elementary introduction to continuous groups and differential invariants; an extensive treatment of groups of motions in euclidean, affine, and riemannian geometry; more. Includes exercises and 62 figures.

Transformation Groups and Representation Theory

Author : T. Tom Dieck
Publisher : Springer
ISBN 13 : 3540385177
Total Pages : 317 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Transformation Groups and Representation Theory by : T. Tom Dieck

Download or read book Transformation Groups and Representation Theory written by T. Tom Dieck and published by Springer. This book was released on 2006-11-15 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction to Compact Transformation Groups

Author :
Publisher : Academic Press
ISBN 13 : 9780080873596
Total Pages : 458 pages
Book Rating : 4.8/5 (735 download)

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Book Synopsis Introduction to Compact Transformation Groups by :

Download or read book Introduction to Compact Transformation Groups written by and published by Academic Press. This book was released on 1972-09-29 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Compact Transformation Groups

Topology of Transitive Transformation Groups

Author : A. L. Onishchik
Publisher :
ISBN 13 :
Total Pages : 324 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Topology of Transitive Transformation Groups by : A. L. Onishchik

Download or read book Topology of Transitive Transformation Groups written by A. L. Onishchik and published by . This book was released on 1994 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Die Soldaten; Eine Komödie

Author : Jakob Michael Reinhold Lenz
Publisher : Megali Verlag
ISBN 13 : 9783387058482
Total Pages : 0 pages
Book Rating : 4.0/5 (584 download)

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Book Synopsis Die Soldaten; Eine Komödie by : Jakob Michael Reinhold Lenz

Download or read book Die Soldaten; Eine Komödie written by Jakob Michael Reinhold Lenz and published by Megali Verlag. This book was released on 2023-09-17 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reproduktion des Originals. Der Verlag Megali spezialisiert sich auf die Reproduktion historischer Werke in Großdruck, um Menschen mit eingeschränkter Sehfähigkeit das Lesen zu erleichtern.

Modern Geometry - Methods and Applications

Author : B.A. Dubrovin
Publisher : Springer Science & Business Media
ISBN 13 : 1468499467
Total Pages : 479 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Modern Geometry - Methods and Applications by : B.A. Dubrovin

Download or read book Modern Geometry - Methods and Applications written by B.A. Dubrovin and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: manifolds, transformation groups, and Lie algebras, as well as the basic concepts of visual topology. It was also agreed that the course should be given in as simple and concrete a language as possible, and that wherever practic able the terminology should be that used by physicists. Thus it was along these lines that the archetypal course was taught. It was given more permanent form as duplicated lecture notes published under the auspices of Moscow State University as: Differential Geometry, Parts I and II, by S. P. Novikov, Division of Mechanics, Moscow State University, 1972. Subsequently various parts of the course were altered, and new topics added. This supplementary material was published (also in duplicated form) as Differential Geometry, Part III, by S. P. Novikov and A. T. Fomenko, Division of Mechanics, Moscow State University, 1974. The present book is the outcome of a reworking, re-ordering, and ex tensive elaboration of the above-mentioned lecture notes. It is the authors' view that it will serve as a basic text from which the essentials for a course in modern geometry may be easily extracted. To S. P. Novikov are due the original conception and the overall plan of the book. The work of organizing the material contained in the duplicated lecture notes in accordance with this plan was carried out by B. A. Dubrovin.

Transformation Groups

Author : Tammo tom Dieck
Publisher : Walter de Gruyter
ISBN 13 : 3110858371
Total Pages : 325 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Transformation Groups by : Tammo tom Dieck

Download or read book Transformation Groups written by Tammo tom Dieck and published by Walter de Gruyter. This book was released on 2011-04-20 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: “This book is a jewel – it explains important, useful and deep topics in Algebraic Topology that you won’t find elsewhere, carefully and in detail.” Prof. Günter M. Ziegler, TU Berlin

Differential Geometry and Lie Groups

Author : Jean Gallier
Publisher : Springer Nature
ISBN 13 : 3030460401
Total Pages : 777 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Differential Geometry and Lie Groups by : Jean Gallier

Download or read book Differential Geometry and Lie Groups written by Jean Gallier and published by Springer Nature. This book was released on 2020-08-14 with total page 777 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers an introduction to differential geometry designed for readers interested in modern geometry processing. Working from basic undergraduate prerequisites, the authors develop manifold theory and Lie groups from scratch; fundamental topics in Riemannian geometry follow, culminating in the theory that underpins manifold optimization techniques. Students and professionals working in computer vision, robotics, and machine learning will appreciate this pathway into the mathematical concepts behind many modern applications. Starting with the matrix exponential, the text begins with an introduction to Lie groups and group actions. Manifolds, tangent spaces, and cotangent spaces follow; a chapter on the construction of manifolds from gluing data is particularly relevant to the reconstruction of surfaces from 3D meshes. Vector fields and basic point-set topology bridge into the second part of the book, which focuses on Riemannian geometry. Chapters on Riemannian manifolds encompass Riemannian metrics, geodesics, and curvature. Topics that follow include submersions, curvature on Lie groups, and the Log-Euclidean framework. The final chapter highlights naturally reductive homogeneous manifolds and symmetric spaces, revealing the machinery needed to generalize important optimization techniques to Riemannian manifolds. Exercises are included throughout, along with optional sections that delve into more theoretical topics. Differential Geometry and Lie Groups: A Computational Perspective offers a uniquely accessible perspective on differential geometry for those interested in the theory behind modern computing applications. Equally suited to classroom use or independent study, the text will appeal to students and professionals alike; only a background in calculus and linear algebra is assumed. Readers looking to continue on to more advanced topics will appreciate the authors’ companion volume Differential Geometry and Lie Groups: A Second Course.

Transformation Groups and Lie Algebras

Author : Nail H Ibragimov
Publisher : World Scientific Publishing Company
ISBN 13 : 9814460869
Total Pages : 196 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Transformation Groups and Lie Algebras by : Nail H Ibragimov

Download or read book Transformation Groups and Lie Algebras written by Nail H Ibragimov and published by World Scientific Publishing Company. This book was released on 2013-05-20 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the extensive experience of teaching for mathematics, physics and engineering students in Russia, USA, South Africa and Sweden. The author provides students and teachers with an easy to follow textbook spanning a variety of topics. The methods of local Lie groups discussed in the book provide universal and effective method for solving nonlinear differential equations analytically. Introduction to approximate transformation groups also contained in the book helps to develop skills in constructing approximate solutions for differential equations with a small parameter.

Cohomological Methods in Transformation Groups

Author : C. Allday
Publisher : Cambridge University Press
ISBN 13 : 0521350220
Total Pages : 486 pages
Book Rating : 4.5/5 (213 download)

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Book Synopsis Cohomological Methods in Transformation Groups by : C. Allday

Download or read book Cohomological Methods in Transformation Groups written by C. Allday and published by Cambridge University Press. This book was released on 1993-07 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an account of the theory of certain types of compact transformation groups, namely those that are susceptible to study using ordinary cohomology theory and rational homotopy theory, which in practice means the torus groups and elementary abelian p-groups. The efforts of many mathematicians have combined to bring a depth of understanding to this area. However to make it reasonably accessible to a wide audience, the authors have streamlined the presentation, referring the reader to the literature for purely technical results and working in a simplified setting where possible. In this way the reader with a relatively modest background in algebraic topology and homology theory can penetrate rather deeply into the subject, whilst the book at the same time makes a useful reference for the more specialised reader.

Transformation Groups Applied to Mathematical Physics

Author : Nail H. Ibragimov
Publisher : Springer Science & Business Media
ISBN 13 : 9781402003394
Total Pages : 422 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Transformation Groups Applied to Mathematical Physics by : Nail H. Ibragimov

Download or read book Transformation Groups Applied to Mathematical Physics written by Nail H. Ibragimov and published by Springer Science & Business Media. This book was released on 2001-11-30 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approach your problems from the right It isn't that they can't see the solution. end and begin with the answers. Then It is that they can't see the problem. one day, perhaps you will find the final question. G.K. Chesterton. The Scandal of Father Brown 'The Point of a Pin'. 'The Hermit Clad in Crane Feathers' in R.van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in - gional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in pack ing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Differential Geometry and Differential Equations

Author : Chaohao Gu
Publisher : Springer
ISBN 13 : 3540478833
Total Pages : 259 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Differential Geometry and Differential Equations by : Chaohao Gu

Download or read book Differential Geometry and Differential Equations written by Chaohao Gu and published by Springer. This book was released on 2006-11-15 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: The DD6 Symposium was, like its predecessors DD1 to DD5 both a research symposium and a summer seminar and concentrated on differential geometry. This volume contains a selection of the invited papers and some additional contributions. They cover recent advances and principal trends in current research in differential geometry.