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Author: Udo Hertrich-Jeromin
Publisher: Cambridge University Press
Published: 2003-08-14
Total Pages: 436
ISBN-13: 9780521535694
DOWNLOAD EBOOK →This book introduces the reader to the geometry of surfaces and submanifolds in the conformal n-sphere.
Author: J. Madore
Publisher: Cambridge University Press
Published: 1999-06-24
Total Pages: 381
ISBN-13: 0521659914
DOWNLOAD EBOOK →A thoroughly revised introduction to non-commutative geometry.
Author: Erwin Kreyszig
Publisher: University of Toronto Press
Published: 1968-12-15
Total Pages: 382
ISBN-13: 1487591055
DOWNLOAD EBOOK →This book provides an introduction to the differential geometry of curves and surfaces in three-dimensional Euclidean space and to n-dimensional Riemannian geometry. Based on Kreyszig's earlier book Differential Geometry, it is presented in a simple and understandable manner with many examples illustrating the ideas, methods, and results. Among the topics covered are vector and tensor algebra, the theory of surfaces, the formulae of Weingarten and Gauss, geodesics, mappings of surfaces and their applications, and global problems. A thorough investigation of Reimannian manifolds is made, including the theory of hypersurfaces. Interesting problems are provided and complete solutions are given at the end of the book together with a list of the more important formulae. Elementary calculus is the sole prerequisite for the understanding of this detailed and complete study in mathematics.
Author: Troy L Story
Publisher: iUniverse
Published: 2005
Total Pages: 165
ISBN-13: 0595339212
DOWNLOAD EBOOK →Introduction to Differential Geometry with applications to Navier-Stokes Dynamics is an invaluable manuscript for anyone who wants to understand and use exterior calculus and differential geometry, the modern approach to calculus and geometry. Author Troy Story makes use of over thirty years of research experience to provide a smooth transition from conventional calculus to exterior calculus and differential geometry, assuming only a knowledge of conventional calculus. Introduction to Differential Geometry with applications to Navier-Stokes Dynamics includes the topics: Geometry, Exterior calculus, Homology and co-homology, Applications of differential geometry and exterior calculus to: Hamiltonian mechanics, geometric optics, irreversible thermodynamics, black hole dynamics, electromagnetism, classical string fields, and Navier-Stokes dynamics.
Author: Luther Pfahler Eisenhart
Publisher:
Published: 1959
Total Pages: 326
ISBN-13:
DOWNLOAD EBOOK →Author: Ethan D. Bloch
Publisher: Springer Science & Business Media
Published: 2011-06-27
Total Pages: 433
ISBN-13: 0817681221
DOWNLOAD EBOOK →The uniqueness of this text in combining geometric topology and differential geometry lies in its unifying thread: the notion of a surface. With numerous illustrations, exercises and examples, the student comes to understand the relationship of the modern abstract approach to geometric intuition. The text is kept at a concrete level, avoiding unnecessary abstractions, yet never sacrificing mathematical rigor. The book includes topics not usually found in a single book at this level.
Author: Thomas A. Ivey
Publisher: American Mathematical Soc.
Published: 2016-12-15
Total Pages: 455
ISBN-13: 1470409860
DOWNLOAD EBOOK →Two central aspects of Cartan's approach to differential geometry are the theory of exterior differential systems (EDS) and the method of moving frames. This book presents thorough and modern treatments of both subjects, including their applications to both classic and contemporary problems in geometry. It begins with the classical differential geometry of surfaces and basic Riemannian geometry in the language of moving frames, along with an elementary introduction to exterior differential systems. Key concepts are developed incrementally, with motivating examples leading to definitions, theorems, and proofs. Once the basics of the methods are established, the authors develop applications and advanced topics. One notable application is to complex algebraic geometry, where they expand and update important results from projective differential geometry. As well, the book features an introduction to G-structures and a treatment of the theory of connections. The techniques of EDS are also applied to obtain explicit solutions of PDEs via Darboux's method, the method of characteristics, and Cartan's method of equivalence. This text is suitable for a one-year graduate course in differential geometry, and parts of it can be used for a one-semester course. It has numerous exercises and examples throughout. It will also be useful to experts in areas such as geometry of PDE systems and complex algebraic geometry who want to learn how moving frames and exterior differential systems apply to their fields. The second edition features three new chapters: on Riemannian geometry, emphasizing the use of representation theory; on the latest developments in the study of Darboux-integrable systems; and on conformal geometry, written in a manner to introduce readers to the related parabolic geometry perspective.
