The Geometry Of The Generalized Gauss Map

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The Geometry of the Generalized Gauss Map

Author : David A. Hoffman
Publisher : American Mathematical Soc.
ISBN 13 : 0821822365
Total Pages : 113 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Geometry of the Generalized Gauss Map by : David A. Hoffman

Download or read book The Geometry of the Generalized Gauss Map written by David A. Hoffman and published by American Mathematical Soc.. This book was released on 1980 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is devoted primarily to the study of properties of the Grassmannian of oriented 2-planes in [double-struck capital]R[superscript]n and to applications of these properties to understanding minimal surfaces in [double-struck capital]R[superscript]n via the generalized Gauss map. The extrinsic geometry of the Grassmannian, when considered as a submanifold of [double-struck capital]CP[superscript]n-2, is investigated, with special emphasis on the nature of the intersection of the Grassmannian with linear subspaces of [double-struck capital]CP[superscript]n-1. These results are the basis for a discussion of minimal surfaces that are degenerate in various ways; understanding the different types of degeneracy and their interrelations is a critical step toward obtaining a clear picture of the basic geometric properties of minimal surfaces in [double-struck capital]R[superscript]n.

Grassmannians and Gauss Maps in Piecewise-Linear Topology

Author : Norman Levitt
Publisher : Springer
ISBN 13 : 3540460780
Total Pages : 208 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Grassmannians and Gauss Maps in Piecewise-Linear Topology by : Norman Levitt

Download or read book Grassmannians and Gauss Maps in Piecewise-Linear Topology written by Norman Levitt and published by Springer. This book was released on 2006-11-14 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book explores the possibility of extending the notions of "Grassmannian" and "Gauss map" to the PL category. They are distinguished from "classifying space" and "classifying map" which are essentially homotopy-theoretic notions. The analogs of Grassmannian and Gauss map defined incorporate geometric and combinatorial information. Principal applications involve characteristic class theory, smoothing theory, and the existence of immersion satifying certain geometric criteria, e.g. curvature conditions. The book assumes knowledge of basic differential topology and bundle theory, including Hirsch-Gromov-Phillips theory, as well as the analogous theories for the PL category. The work should be of interest to mathematicians concerned with geometric topology, PL and PD aspects of differential geometry and the geometry of polyhedra.

Value Distribution Theory of the Gauss Map of Minimal Surfaces in Rm

Author : Hirotaka Fujimoto
Publisher : Springer Science & Business Media
ISBN 13 : 332280271X
Total Pages : 222 pages
Book Rating : 4.3/5 (228 download)

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Book Synopsis Value Distribution Theory of the Gauss Map of Minimal Surfaces in Rm by : Hirotaka Fujimoto

Download or read book Value Distribution Theory of the Gauss Map of Minimal Surfaces in Rm written by Hirotaka Fujimoto and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents in a systematic and almost self-contained way the striking analogy between classical function theory, in particular the value distribution theory of holomorphic curves in projective space, on the one hand, and important and beautiful properties of the Gauss map of minimal surfaces on the other hand. Both theories are developed in the text, including many results of recent research. The relations and analogies between them become completely clear. The book is written for interested graduate students and mathematicians, who want to become more familiar with this modern development in the two classical areas of mathematics, but also for those, who intend to do further research on minimal surfaces.

Differential Geometry of Varieties with Degenerate Gauss Maps

Author : Maks A. Akivis
Publisher : Springer Science & Business Media
ISBN 13 : 0387215115
Total Pages : 272 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Differential Geometry of Varieties with Degenerate Gauss Maps by : Maks A. Akivis

Download or read book Differential Geometry of Varieties with Degenerate Gauss Maps written by Maks A. Akivis and published by Springer Science & Business Media. This book was released on 2006-04-18 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book surveys the differential geometry of varieties with degenerate Gauss maps, using moving frames and exterior differential forms as well as tensor methods. The authors illustrate the structure of varieties with degenerate Gauss maps, determine the singular points and singular varieties, find focal images and construct a classification of the varieties with degenerate Gauss maps.

Harmonic Maps

Author : James Eells
Publisher : World Scientific
ISBN 13 : 9789810207045
Total Pages : 472 pages
Book Rating : 4.2/5 (7 download)

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Book Synopsis Harmonic Maps by : James Eells

Download or read book Harmonic Maps written by James Eells and published by World Scientific. This book was released on 1992 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: These original research papers, written during a period of over a quarter of a century, have two main objectives. The first is to lay the foundations of the theory of harmonic maps between Riemannian Manifolds, and the second to establish various existence and regularity theorems as well as the explicit constructions of such maps.

The Geometry of Submanifolds

Author : Yu. Aminov
Publisher : CRC Press
ISBN 13 : 1482296861
Total Pages : 388 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis The Geometry of Submanifolds by : Yu. Aminov

Download or read book The Geometry of Submanifolds written by Yu. Aminov and published by CRC Press. This book was released on 2001-01-11 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a comprehensive presentation of the geometry of submanifolds that expands on classical results in the theory of curves and surfaces. The geometry of submanifolds starts from the idea of the extrinsic geometry of a surface, and the theory studies the position and properties of a submanifold in ambient space in both local and global aspects.

Geometry Symposium Utrecht 1980

Author : E. Looijenga
Publisher : Springer
ISBN 13 : 3540386416
Total Pages : 162 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Geometry Symposium Utrecht 1980 by : E. Looijenga

Download or read book Geometry Symposium Utrecht 1980 written by E. Looijenga and published by Springer. This book was released on 2006-11-14 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Contemporary Aspects of Complex Analysis, Differential Geometry and Mathematical Physics

Author :
Publisher :
ISBN 13 : 9814479977
Total Pages : pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Contemporary Aspects of Complex Analysis, Differential Geometry and Mathematical Physics by :

Download or read book Contemporary Aspects of Complex Analysis, Differential Geometry and Mathematical Physics written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Geometry V

Author : Robert Osserman
Publisher : Springer Science & Business Media
ISBN 13 : 9783540605232
Total Pages : 300 pages
Book Rating : 4.6/5 (52 download)

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Book Synopsis Geometry V by : Robert Osserman

Download or read book Geometry V written by Robert Osserman and published by Springer Science & Business Media. This book was released on 1997-10-09 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Few people outside of mathematics are aware of the varieties of mathemat ical experience - the degree to which different mathematical subjects have different and distinctive flavors, often attractive to some mathematicians and repellant to others. The particular flavor of the subject of minimal surfaces seems to lie in a combination of the concreteness of the objects being studied, their origin and relation to the physical world, and the way they lie at the intersection of so many different parts of mathematics. In the past fifteen years a new component has been added: the availability of computer graphics to provide illustrations that are both mathematically instructive and esthetically pleas ing. During the course of the twentieth century, two major thrusts have played a seminal role in the evolution of minimal surface theory. The first is the work on the Plateau Problem, whose initial phase culminated in the solution for which Jesse Douglas was awarded one of the first two Fields Medals in 1936. (The other Fields Medal that year went to Lars V. Ahlfors for his contributions to complex analysis, including his important new insights in Nevanlinna Theory.) The second was the innovative approach to partial differential equations by Serge Bernstein, which led to the celebrated Bernstein's Theorem, stating that the only solution to the minimal surface equation over the whole plane is the trivial solution: a linear function.

Harmonic Maps

Author : James Eells
Publisher : World Scientific
ISBN 13 : 9814506125
Total Pages : 452 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Harmonic Maps by : James Eells

Download or read book Harmonic Maps written by James Eells and published by World Scientific. This book was released on 1992-08-21 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: These original research papers, written during a period of over a quarter of a century, have two main objectives. The first is to lay the foundations of the theory of harmonic maps between Riemannian Manifolds, and the second to establish various existence and regularity theorems as well as the explicit constructions of such maps. Contents:Harmonic Mappings of Riemannian Manifolds (1964)Énergie et Déformations en Géométrie Différentielle (1964)Variational Theory in Fibre Bundles (1965)Restrictions on Harmonic Maps of Surfaces (1976)The Surfaces of Delaunay (1987)Minimal Graphs (1979)On the Construction of Harmonic and Holomorphic Maps between Surfaces (1980)Deformations of Metrics and Associated Harmonic Maps (1981)A Conservation Law for Harmonic Maps (1981)Maps of Minimum Energy (1981)The Existence and Construction of Certain Harmonic Maps (1982)Harmonic Maps from Surfaces to Complex Projective Spaces (1983)Examples of Harmonic Maps from Disks to Hemispheres (1984)Variational Theory in Fibre Bundles: Examples (1983)Constructions Twistorielles des Applications Harmoniques (1983)Removable Singularities of Harmonic Maps (1984)On Equivariant Harmonic Maps (1984)Regularity of Certain Harmonic Maps (1984)Gauss Maps of Surfaces (1984)Minimal Branched Immersions into Three-Manifolds (1985)Twistorial Construction of Harmonic Maps of Surfaces into Four-Manifolds (1985)Certain Variational Principles in Riemannian Geometry (1985)Harmonic Maps and Minimal Surface Coboundaries (1987)Unstable Minimal Surface Coboundaries (1986)Harmonic Maps between Spheres and Ellipsoids (1990)On Representing Homotopy Classes by Harmonic Maps (1991) Readership: Researchers and students in differential geometry and topology and theoretical physicists. keywords:Harmonic Mapping;Energy;Holomorphic Map;First (Second) Variation of Energy;Minimal Immersion;Minimal Graph;Regularity of Maps;Removable Singularities“It is striking that the papers cut a wide swathe through mathematics, and this is a testimony to the fact that the author has influenced so many younger mathematicians, several of whom are represented here.”Mathematical Reviews

Recent Developments in Geometry

Author : Robert Everist Greene
Publisher : American Mathematical Soc.
ISBN 13 : 0821851071
Total Pages : 354 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Recent Developments in Geometry by : Robert Everist Greene

Download or read book Recent Developments in Geometry written by Robert Everist Greene and published by American Mathematical Soc.. This book was released on 1989 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the outgrowth of a Special Session on Geometry, held at the November 1987 meeting of the AMS at the University of California at Los Angeles. The unusually well-attended session attracted more than sixty participants and featured over forty addresses by some of the day's outstanding geometers. By common consent, it was decided that the papers to be collected in the present volume should be surveys of relatively broad areas of geometry, rather than detailed presentations of new research results. A comprehensive survey of the field is beyond the scope of a volume such as this. Nonetheless, the editors have sought to provide all geometers, whatever their specialties, with some insight into recent developments in a variety of topics in this active area of research.

Computer Algebra in Scientific Computing

Author : Andreas Weber
Publisher : MDPI
ISBN 13 : 3039217305
Total Pages : 160 pages
Book Rating : 4.0/5 (392 download)

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Book Synopsis Computer Algebra in Scientific Computing by : Andreas Weber

Download or read book Computer Algebra in Scientific Computing written by Andreas Weber and published by MDPI. This book was released on 2019-11-04 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although scientific computing is very often associated with numeric computations, the use of computer algebra methods in scientific computing has obtained considerable attention in the last two decades. Computer algebra methods are especially suitable for parametric analysis of the key properties of systems arising in scientific computing. The expression-based computational answers generally provided by these methods are very appealing as they directly relate properties to parameters and speed up testing and tuning of mathematical models through all their possible behaviors. This book contains 8 original research articles dealing with a broad range of topics, ranging from algorithms, data structures, and implementation techniques for high-performance sparse multivariate polynomial arithmetic over the integers and rational numbers over methods for certifying the isolated zeros of polynomial systems to computer algebra problems in quantum computing.

Harmonic Mappings and Minimal Immersion

Author : Enrico Giusti
Publisher : Springer
ISBN 13 : 3540397167
Total Pages : 295 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Harmonic Mappings and Minimal Immersion by : Enrico Giusti

Download or read book Harmonic Mappings and Minimal Immersion written by Enrico Giusti and published by Springer. This book was released on 2006-11-14 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Differential Geometry

Author : Ion Mihai
Publisher : MDPI
ISBN 13 : 303921800X
Total Pages : 166 pages
Book Rating : 4.0/5 (392 download)

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Book Synopsis Differential Geometry by : Ion Mihai

Download or read book Differential Geometry written by Ion Mihai and published by MDPI. This book was released on 2019-11-21 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book contains 14 papers published in the Special Issue “Differential Geometry” of the journal Mathematics. They represent a selection of the 30 submissions. This book covers a variety of both classical and modern topics in differential geometry. We mention properties of both rectifying and affine curves, the geometry of hypersurfaces, angles in Minkowski planes, Euclidean submanifolds, differential operators and harmonic forms on Riemannian manifolds, complex manifolds, contact manifolds (in particular, Sasakian and trans-Sasakian manifolds), curvature invariants, and statistical manifolds and their submanifolds (in particular, Hessian manifolds). We wish to mention that among the authors, there are both well-known geometers and young researchers. The authors are from countries with a tradition in differential geometry: Belgium, China, Greece, Japan, Korea, Poland, Romania, Spain, Turkey, and United States of America. Many of these papers were already cited by other researchers in their articles. This book is useful for specialists in differential geometry, operator theory, physics, and information geometry as well as graduate students in mathematics.

Harmonic Mappings, Twistors And Sigma Models

Author : Paul Gauduchon
Publisher : World Scientific
ISBN 13 : 9813201487
Total Pages : 390 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Harmonic Mappings, Twistors And Sigma Models by : Paul Gauduchon

Download or read book Harmonic Mappings, Twistors And Sigma Models written by Paul Gauduchon and published by World Scientific. This book was released on 1988-10-01 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Harmonic mappings have played in recent years and will likely to play in the future an important role in Differential Geometry and Theoretical Physics, where they are known as s-models. These Proceedings develop both aspects of the theory, with a special attention to the constructive methods, in particular the so-called twistorial approach. It includes expository articles on the twistorial methods, the various appearence of σ-models in Physics, the powerful analytic theory of regularity of SCHOEN-UHLENBECK.

A Survey of Minimal Surfaces

Author : Robert Osserman
Publisher : Courier Corporation
ISBN 13 : 0486167690
Total Pages : 224 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis A Survey of Minimal Surfaces by : Robert Osserman

Download or read book A Survey of Minimal Surfaces written by Robert Osserman and published by Courier Corporation. This book was released on 2013-12-10 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Newly updated accessible study covers parametric and non-parametric surfaces, isothermal parameters, Bernstein’s theorem, much more, including such recent developments as new work on Plateau’s problem and on isoperimetric inequalities. Clear, comprehensive examination provides profound insights into crucial area of pure mathematics. 1986 edition. Index.

Issues in General and Specialized Mathematics Research: 2011 Edition

Author :
Publisher : ScholarlyEditions
ISBN 13 : 1464964920
Total Pages : 1326 pages
Book Rating : 4.4/5 (649 download)

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Book Synopsis Issues in General and Specialized Mathematics Research: 2011 Edition by :

Download or read book Issues in General and Specialized Mathematics Research: 2011 Edition written by and published by ScholarlyEditions. This book was released on 2012-01-09 with total page 1326 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in General and Specialized Mathematics Research: 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about General and Specialized Mathematics Research. The editors have built Issues in General and Specialized Mathematics Research: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about General and Specialized Mathematics Research in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in General and Specialized Mathematics Research: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.