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| Author | : Lyndon Woodward |
| Publisher | : Cambridge University Press |
| Total Pages | : 275 |
| Release | : 2019 |
| Genre | : Mathematics |
| ISBN | : 1108424937 |
With detailed explanations and numerous examples, this textbook covers the differential geometry of surfaces in Euclidean space.
| Author | : Thierry Aubin |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 198 |
| Release | : 2001 |
| Genre | : Mathematics |
| ISBN | : 082182709X |
This textbook for second-year graduate students is intended as an introduction to differential geometry with principal emphasis on Riemannian geometry. Chapter I explains basic definitions and gives the proofs of the important theorems of Whitney and Sard. Chapter II deals with vector fields and differential forms. Chapter III addresses integration of vector fields and p-plane fields. Chapter IV develops the notion of connection on a Riemannian manifold considered as a means to define parallel transport on the manifold. The author also discusses related notions of torsion and curvature, and gives a working knowledge of the covariant derivative. Chapter V specializes on Riemannian manifolds by deducing global properties from local properties of curvature, the final goal being to determine the manifold completely. Chapter VI explores some problems in PDEs suggested by the geometry of manifolds. The author is well-known for his significant contributions to the field of geometry and PDEs - particularly for his work on the Yamabe problem - and for his expository accounts on the subject. The text contains many problems and solutions, permitting the reader to apply the theorems and to see concrete developments of the abstract theory.
| Author | : |
| Publisher | : |
| Total Pages | : 343 |
| Release | : 1997 |
| Genre | : Geometry, Differential |
| ISBN | : 9781571462800 |
| Author | : W. Klingenberg |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 188 |
| Release | : 2013-03-14 |
| Genre | : Mathematics |
| ISBN | : 1461299233 |
This English edition could serve as a text for a first year graduate course on differential geometry, as did for a long time the Chicago Notes of Chern mentioned in the Preface to the German Edition. Suitable references for ordin ary differential equations are Hurewicz, W. Lectures on ordinary differential equations. MIT Press, Cambridge, Mass., 1958, and for the topology of surfaces: Massey, Algebraic Topology, Springer-Verlag, New York, 1977. Upon David Hoffman fell the difficult task of transforming the tightly constructed German text into one which would mesh well with the more relaxed format of the Graduate Texts in Mathematics series. There are some e1aborations and several new figures have been added. I trust that the merits of the German edition have survived whereas at the same time the efforts of David helped to elucidate the general conception of the Course where we tried to put Geometry before Formalism without giving up mathematical rigour. 1 wish to thank David for his work and his enthusiasm during the whole period of our collaboration. At the same time I would like to commend the editors of Springer-Verlag for their patience and good advice. Bonn Wilhelm Klingenberg June,1977 vii From the Preface to the German Edition This book has its origins in a one-semester course in differential geometry which 1 have given many times at Gottingen, Mainz, and Bonn.
| Author | : Ethan D. Bloch |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 433 |
| Release | : 2011-06-27 |
| Genre | : Mathematics |
| ISBN | : 0817681221 |
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 | : Vaisman |
| Publisher | : CRC Press |
| Total Pages | : 188 |
| Release | : 1983-12-13 |
| Genre | : Mathematics |
| ISBN | : 9780824770631 |
This book proposes a new approach which is designed to serve as an introductory course in differential geometry for advanced undergraduate students. It is based on lectures given by the author at several universities, and discusses calculus, topology, and linear algebra.
| Author | : Dorairaj Somasundaram |
| Publisher | : Alpha Science Int'l Ltd. |
| Total Pages | : 472 |
| Release | : 2005 |
| Genre | : Computers |
| ISBN | : 9781842651827 |
Differential Geometry: A First Course is an introduction to the classical theory of space curves and surfaces offered in graduate and postgraduate courses in mathematics. Based on Serret-Frenet formulae, the theory of space curves is developed and concluded with a detailed discussion on fundamental existence theorem. The theory of surfaces includes the first fundamental form with local intrinsic properties, geodesics on surfaces, the second fundamental form with local non-intrinsic properties and the fundamental equations of the surface theory with several applications.
| Author | : Andrew McInerney |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 420 |
| Release | : 2013-07-09 |
| Genre | : Mathematics |
| ISBN | : 1461477328 |
Differential geometry arguably offers the smoothest transition from the standard university mathematics sequence of the first four semesters in calculus, linear algebra, and differential equations to the higher levels of abstraction and proof encountered at the upper division by mathematics majors. Today it is possible to describe differential geometry as "the study of structures on the tangent space," and this text develops this point of view. This book, unlike other introductory texts in differential geometry, develops the architecture necessary to introduce symplectic and contact geometry alongside its Riemannian cousin. The main goal of this book is to bring the undergraduate student who already has a solid foundation in the standard mathematics curriculum into contact with the beauty of higher mathematics. In particular, the presentation here emphasizes the consequences of a definition and the careful use of examples and constructions in order to explore those consequences.
| Author | : S. Kumaresan |
| Publisher | : Springer |
| Total Pages | : 306 |
| Release | : 2002-01-15 |
| Genre | : Mathematics |
| ISBN | : 9386279088 |
| Author | : A.N. Pressley |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 469 |
| Release | : 2010-03-10 |
| Genre | : Mathematics |
| ISBN | : 1848828918 |
Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces suitable for a first course on the subject. Prerequisites are kept to an absolute minimum – nothing beyond first courses in linear algebra and multivariable calculus – and the most direct and straightforward approach is used throughout. New features of this revised and expanded second edition include: a chapter on non-Euclidean geometry, a subject that is of great importance in the history of mathematics and crucial in many modern developments. The main results can be reached easily and quickly by making use of the results and techniques developed earlier in the book. Coverage of topics such as: parallel transport and its applications; map colouring; holonomy and Gaussian curvature. Around 200 additional exercises, and a full solutions manual for instructors, available via www.springer.com ul
