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Differential And Complex Geometry Origins Abstractions And Embeddings
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Book Synopsis Differential and Complex Geometry: Origins, Abstractions and Embeddings by : Raymond O. Wells, Jr.
Download or read book Differential and Complex Geometry: Origins, Abstractions and Embeddings written by Raymond O. Wells, Jr. and published by Springer. This book was released on 2017-08-01 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential and complex geometry are two central areas of mathematics with a long and intertwined history. This book, the first to provide a unified historical perspective of both subjects, explores their origins and developments from the sixteenth to the twentieth century. Providing a detailed examination of the seminal contributions to differential and complex geometry up to the twentieth-century embedding theorems, this monograph includes valuable excerpts from the original documents, including works of Descartes, Fermat, Newton, Euler, Huygens, Gauss, Riemann, Abel, and Nash. Suitable for beginning graduate students interested in differential, algebraic or complex geometry, this book will also appeal to more experienced readers.
Book Synopsis Transcendence and Linear Relations of 1-Periods by : Annette Huber
Download or read book Transcendence and Linear Relations of 1-Periods written by Annette Huber and published by Cambridge University Press. This book was released on 2022-05-26 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Leading experts explore the relation between periods and transcendental numbers, using a modern approach derived from the theory of motives.
Book Synopsis Complex Differential Geometry by : Fangyang Zheng
Download or read book Complex Differential Geometry written by Fangyang Zheng and published by . This book was released on 2000 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Visual Differential Geometry and Forms by : Tristan Needham
Download or read book Visual Differential Geometry and Forms written by Tristan Needham and published by Princeton University Press. This book was released on 2021-07-13 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: An inviting, intuitive, and visual exploration of differential geometry and forms Visual Differential Geometry and Forms fulfills two principal goals. In the first four acts, Tristan Needham puts the geometry back into differential geometry. Using 235 hand-drawn diagrams, Needham deploys Newton’s geometrical methods to provide geometrical explanations of the classical results. In the fifth act, he offers the first undergraduate introduction to differential forms that treats advanced topics in an intuitive and geometrical manner. Unique features of the first four acts include: four distinct geometrical proofs of the fundamentally important Global Gauss-Bonnet theorem, providing a stunning link between local geometry and global topology; a simple, geometrical proof of Gauss’s famous Theorema Egregium; a complete geometrical treatment of the Riemann curvature tensor of an n-manifold; and a detailed geometrical treatment of Einstein’s field equation, describing gravity as curved spacetime (General Relativity), together with its implications for gravitational waves, black holes, and cosmology. The final act elucidates such topics as the unification of all the integral theorems of vector calculus; the elegant reformulation of Maxwell’s equations of electromagnetism in terms of 2-forms; de Rham cohomology; differential geometry via Cartan’s method of moving frames; and the calculation of the Riemann tensor using curvature 2-forms. Six of the seven chapters of Act V can be read completely independently from the rest of the book. Requiring only basic calculus and geometry, Visual Differential Geometry and Forms provocatively rethinks the way this important area of mathematics should be considered and taught.
Book Synopsis Advances in Discrete Differential Geometry by : Alexander I. Bobenko
Download or read book Advances in Discrete Differential Geometry written by Alexander I. Bobenko and published by Springer. This book was released on 2016-08-12 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, and on pure mathematics and its practical applications. The interaction of these facets is demonstrated by concrete examples, including discrete conformal mappings, discrete complex analysis, discrete curvatures and special surfaces, discrete integrable systems, conformal texture mappings in computer graphics, and free-form architecture. This richly illustrated book will convince readers that this new branch of mathematics is both beautiful and useful. It will appeal to graduate students and researchers in differential geometry, complex analysis, mathematical physics, numerical methods, discrete geometry, as well as computer graphics and geometry processing.
Book Synopsis Global Differential Geometry by : Alfred Gray
Download or read book Global Differential Geometry written by Alfred Gray and published by American Mathematical Soc.. This book was released on 2001 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: Consists of 15 invited papers and 40 posters presented at the September 2000 conference. Many of the presentations deal with Riemannian manifolds, homogenous spaces, complex structures, symplectic manifolds, the geometry of geodesic spheres and tubes, the geometry of surfaces, and computer graphics in differential geometry. Some example topics are osculating tubes and self-linking for curves on the three-sphere, the Seiberg-Witten equations and almost- Hermitian geometry, complex geometry and representation of Lie groups, isometric immersions without positive Ricci curvature, and Weil algebras of generalized higher order velocities bundles. No index. c. Book News Inc.
Book Synopsis Classical and Discrete Differential Geometry by : David Xianfeng Gu
Download or read book Classical and Discrete Differential Geometry written by David Xianfeng Gu and published by CRC Press. This book was released on 2023-01-31 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces differential geometry and cutting-edge findings from the discipline by incorporating both classical approaches and modern discrete differential geometry across all facets and applications, including graphics and imaging, physics and networks. With curvature as the centerpiece, the authors present the development of differential geometry, from curves to surfaces, thence to higher dimensional manifolds; and from smooth structures to metric spaces, weighted manifolds and complexes, and to images, meshes and networks. The first part of the book is a differential geometric study of curves and surfaces in the Euclidean space, enhanced while the second part deals with higher dimensional manifolds centering on curvature by exploring the various ways of extending it to higher dimensional objects and more general structures and how to return to lower dimensional constructs. The third part focuses on computational algorithms in algebraic topology and conformal geometry, applicable for surface parameterization, shape registration and structured mesh generation. The volume will be a useful reference for students of mathematics and computer science, as well as researchers and engineering professionals who are interested in graphics and imaging, complex networks, differential geometry and curvature.
Book Synopsis Differential Geometry and Topology, Discrete and Computational Geometry by : Mohamed Boucetta
Download or read book Differential Geometry and Topology, Discrete and Computational Geometry written by Mohamed Boucetta and published by IOS Press. This book was released on with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Differential Geometry by : Clifford Henry Taubes
Download or read book Differential Geometry written by Clifford Henry Taubes and published by OUP Oxford. This book was released on 2011-10-13 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bundles, connections, metrics and curvature are the 'lingua franca' of modern differential geometry and theoretical physics. This book will supply a graduate student in mathematics or theoretical physics with the fundamentals of these objects. Many of the tools used in differential topology are introduced and the basic results about differentiable manifolds, smooth maps, differential forms, vector fields, Lie groups, and Grassmanians are all presented here. Other material covered includes the basic theorems about geodesics and Jacobi fields, the classification theorem for flat connections, the definition of characteristic classes, and also an introduction to complex and Kähler geometry. Differential Geometry uses many of the classical examples from, and applications of, the subjects it covers, in particular those where closed form expressions are available, to bring abstract ideas to life. Helpfully, proofs are offered for almost all assertions throughout. All of the introductory material is presented in full and this is the only such source with the classical examples presented in detail.
Book Synopsis Complex Analytic and Differential Geometry by : Jean-Pierre Demailly
Download or read book Complex Analytic and Differential Geometry written by Jean-Pierre Demailly and published by . This book was released on 1997 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Introduction to Differential Geometry by : T. J. Willmore
Download or read book An Introduction to Differential Geometry written by T. J. Willmore and published by Courier Corporation. This book was released on 2013-05-13 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text employs vector methods to explore the classical theory of curves and surfaces. Topics include basic theory of tensor algebra, tensor calculus, calculus of differential forms, and elements of Riemannian geometry. 1959 edition.
Book Synopsis Differential Geometry and Topology by : Jacob T. Schwartz
Download or read book Differential Geometry and Topology written by Jacob T. Schwartz and published by M.E. Sharpe. This book was released on 1968 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Introduction to Differential Geometry with Applications to Elasticity by : Philippe G. Ciarlet
Download or read book An Introduction to Differential Geometry with Applications to Elasticity written by Philippe G. Ciarlet and published by Springer Science & Business Media. This book was released on 2006-06-28 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: curvilinear coordinates. This treatment includes in particular a direct proof of the three-dimensional Korn inequality in curvilinear coordinates. The fourth and last chapter, which heavily relies on Chapter 2, begins by a detailed description of the nonlinear and linear equations proposed by W.T. Koiter for modeling thin elastic shells. These equations are “two-dimensional”, in the sense that they are expressed in terms of two curvilinear coordinates used for de?ning the middle surface of the shell. The existence, uniqueness, and regularity of solutions to the linear Koiter equations is then established, thanks this time to a fundamental “Korn inequality on a surface” and to an “in?nit- imal rigid displacement lemma on a surface”. This chapter also includes a brief introduction to other two-dimensional shell equations. Interestingly, notions that pertain to di?erential geometry per se,suchas covariant derivatives of tensor ?elds, are also introduced in Chapters 3 and 4, where they appear most naturally in the derivation of the basic boundary value problems of three-dimensional elasticity and shell theory. Occasionally, portions of the material covered here are adapted from - cerpts from my book “Mathematical Elasticity, Volume III: Theory of Shells”, published in 2000by North-Holland, Amsterdam; in this respect, I am indebted to Arjen Sevenster for his kind permission to rely on such excerpts. Oth- wise, the bulk of this work was substantially supported by two grants from the Research Grants Council of Hong Kong Special Administrative Region, China [Project No. 9040869, CityU 100803 and Project No. 9040966, CityU 100604].
Book Synopsis Differential Geometry by : L. A. Cordero
Download or read book Differential Geometry written by L. A. Cordero and published by Pitman Advanced Publishing Program. This book was released on 1985 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Differential Geometry on Complex and Almost Complex Spaces by : Kentarō Yano
Download or read book Differential Geometry on Complex and Almost Complex Spaces written by Kentarō Yano and published by . This book was released on 1965 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Perspectives on Projective Geometry by : J Rgen Richter-Gebert
Download or read book Perspectives on Projective Geometry written by J Rgen Richter-Gebert and published by Springer. This book was released on 2016-05-01 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive introduction into the classical topic of projective geometry. It explains how metric concepts may be best understood in projective terms and explores the beauty of the interplay of geometry, algebra and combinatorics."
Book Synopsis An Introduction To Differential Geometry by : Amur
Download or read book An Introduction To Differential Geometry written by Amur and published by . This book was released on 2010 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt:
