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Author : Udo Hertrich-Jeromin
Publisher : Cambridge University Press
Page : 436 pages
File Size : 54,8 Mb
Release : 2003-08-14
Category : Mathematics
ISBN : 0521535697
This book introduces the reader to the geometry of surfaces and submanifolds in the conformal n-sphere.
Author : Wang Rong,Chen Yue
Publisher : World Scientific
Page : 222 pages
File Size : 45,9 Mb
Release : 1999-01-18
Category : Mathematics
ISBN : 9789814495806
This book gives an outline of the developments of differential geometry and topology in the twentieth century, especially those which will be closely related to new discoveries in theoretical physics.
Author : Michael Spivak
Publisher : Unknown
Page : 702 pages
File Size : 40,6 Mb
Release : 1979
Category : Mathematics
ISBN : UOM:39015062882942
Author : Gal Gross,Eckhard Meinrenken
Publisher : Springer Nature
Page : 348 pages
File Size : 43,9 Mb
Release : 2023-04-25
Category : Mathematics
ISBN : 9783031254093
This textbook serves as an introduction to modern differential geometry at a level accessible to advanced undergraduate and master's students. It places special emphasis on motivation and understanding, while developing a solid intuition for the more abstract concepts. In contrast to graduate level references, the text relies on a minimal set of prerequisites: a solid grounding in linear algebra and multivariable calculus, and ideally a course on ordinary differential equations. Manifolds are introduced intrinsically in terms of coordinate patches glued by transition functions. The theory is presented as a natural continuation of multivariable calculus; the role of point-set topology is kept to a minimum. Questions sprinkled throughout the text engage students in active learning, and encourage classroom participation. Answers to these questions are provided at the end of the book, thus making it ideal for independent study. Material is further reinforced with homework problems ranging from straightforward to challenging. The book contains more material than can be covered in a single semester, and detailed suggestions for instructors are provided in the Preface.
Author : Thomas James Willmore
Publisher : Unknown
Page : 317 pages
File Size : 47,8 Mb
Release : 1966
Category : Electronic
ISBN : OCLC:1067875079
Author : Troy L Story
Publisher : iUniverse
Page : 165 pages
File Size : 43,7 Mb
Release : 2005
Category : Geometry, Differential
ISBN : 9780595339211
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 : Amur
Publisher : Unknown
Page : 241 pages
File Size : 44,8 Mb
Release : 2010
Category : Geometry, Differential
ISBN : 8184870507
Author : Luther Pfahler Eisenhart
Publisher : Unknown
Page : 328 pages
File Size : 47,7 Mb
Release : 1947
Category : Mathematics
ISBN : UOM:39015000968498
Author : Joel W. Robbin,Dietmar A. Salamon
Publisher : Springer Spektrum
Page : 418 pages
File Size : 41,8 Mb
Release : 2022-01-13
Category : Mathematics
ISBN : 3662643391
This textbook is suitable for a one semester lecture course on differential geometry for students of mathematics or STEM disciplines with a working knowledge of analysis, linear algebra, complex analysis, and point set topology. The book treats the subject both from an extrinsic and an intrinsic view point. The first chapters give a historical overview of the field and contain an introduction to basic concepts such as manifolds and smooth maps, vector fields and flows, and Lie groups, leading up to the theorem of Frobenius. Subsequent chapters deal with the Levi-Civita connection, geodesics, the Riemann curvature tensor, a proof of the Cartan-Ambrose-Hicks theorem, as well as applications to flat spaces, symmetric spaces, and constant curvature manifolds. Also included are sections about manifolds with nonpositive sectional curvature, the Ricci tensor, the scalar curvature, and the Weyl tensor. An additional chapter goes beyond the scope of a one semester lecture course and deals with subjects such as conjugate points and the Morse index, the injectivity radius, the group of isometries and the Myers-Steenrod theorem, and Donaldson's differential geometric approach to Lie algebra theory.
Author : J. Madore
Publisher : Cambridge University Press
Page : 381 pages
File Size : 41,7 Mb
Release : 1999-06-24
Category : Mathematics
ISBN : 9780521659918
A thoroughly revised introduction to non-commutative geometry.
Author : Anders Kock
Publisher : Cambridge University Press
Page : 245 pages
File Size : 55,8 Mb
Release : 2006-06-22
Category : Mathematics
ISBN : 9780521687386
This book, first published in 2006, details how limit processes can be represented algebraically.
Author : Luther Pfahler Eisenhart
Publisher : Unknown
Page : 320 pages
File Size : 55,9 Mb
Release : 2014-07
Category : Calculus of tensors
ISBN : 0486780597
Having introduced a generation of students to the serious mathematics of relativity theory and Riemannian geometry, this volume remains a valuable guide to today's advanced undergraduates and graduate students. Topics include curves in space, transformation of coordinates, tensor calculus, intrinsic geometry of a surface, and surfaces in space. 1947 edition.
Author : Alexander I. Bobenko
Publisher : Springer
Page : 441 pages
File Size : 45,9 Mb
Release : 2016-08-12
Category : Mathematics
ISBN : 9783662504475
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.
Author : T. (Thomas) Willmore
Publisher : Unknown
Page : 317 pages
File Size : 42,6 Mb
Release : 1959
Category : Electronic
ISBN : OCLC:816926608
Author : Rong Wang,Yue Chen
Publisher : World Scientific
Page : 228 pages
File Size : 46,9 Mb
Release : 1998
Category : Science
ISBN : 9810235593
This book gives an outline of the developments of differential geometry and topology in the twentieth century, especially those which will be closely related to new discoveries in theoretical physics.