Contact Manifolds in Riemannian Geometry
Author: D. E. Blair
Publisher: Springer
Published: 2006-11-14
Total Pages: 153
ISBN-13: 3540381546
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Riemannian Geometry of Contact and Symplectic Manifolds
Author: David E. Blair
Publisher: Springer Science & Business Media
Published: 2013-11-11
Total Pages: 263
ISBN-13: 1475736045
DOWNLOAD EBOOKBook endorsed by the Sunyer Prize Committee (A. Weinstein, J. Oesterle et. al.).
Riemannian Manifolds
Author: John M. Lee
Publisher: Springer Science & Business Media
Published: 2006-04-06
Total Pages: 232
ISBN-13: 0387227261
DOWNLOAD EBOOKThis text focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. It covers proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet’s Theorem, and a special case of the Cartan-Ambrose-Hicks Theorem.
On the Hypotheses Which Lie at the Bases of Geometry
Author: Bernhard Riemann
Publisher: Birkhäuser
Published: 2016-04-19
Total Pages: 181
ISBN-13: 3319260421
DOWNLOAD EBOOKThis book presents William Clifford’s English translation of Bernhard Riemann’s classic text together with detailed mathematical, historical and philosophical commentary. The basic concepts and ideas, as well as their mathematical background, are provided, putting Riemann’s reasoning into the more general and systematic perspective achieved by later mathematicians and physicists (including Helmholtz, Ricci, Weyl, and Einstein) on the basis of his seminal ideas. Following a historical introduction that positions Riemann’s work in the context of his times, the history of the concept of space in philosophy, physics and mathematics is systematically presented. A subsequent chapter on the reception and influence of the text accompanies the reader from Riemann’s times to contemporary research. Not only mathematicians and historians of the mathematical sciences, but also readers from other disciplines or those with an interest in physics or philosophy will find this work both appealing and insightful.
Introduction to Riemannian Manifolds
Author: John M. Lee
Publisher: Springer
Published: 2019-01-02
Total Pages: 447
ISBN-13: 3319917552
DOWNLOAD EBOOKThis text focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. It covers proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet’s Theorem, and a special case of the Cartan-Ambrose-Hicks Theorem.
First Steps in Differential Geometry
Author: Andrew McInerney
Publisher: Springer Science & Business Media
Published: 2013-07-09
Total Pages: 420
ISBN-13: 1461477328
DOWNLOAD EBOOKDifferential 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.
An Introduction to Differentiable Manifolds and Riemannian Geometry
Author:
Publisher: Academic Press
Published: 1975-08-22
Total Pages: 441
ISBN-13: 0080873790
DOWNLOAD EBOOKAn Introduction to Differentiable Manifolds and Riemannian Geometry
An Introduction to Riemannian Geometry
Author: Leonor Godinho
Publisher: Springer
Published: 2014-07-26
Total Pages: 476
ISBN-13: 3319086669
DOWNLOAD EBOOKUnlike many other texts on differential geometry, this textbook also offers interesting applications to geometric mechanics and general relativity. The first part is a concise and self-contained introduction to the basics of manifolds, differential forms, metrics and curvature. The second part studies applications to mechanics and relativity including the proofs of the Hawking and Penrose singularity theorems. It can be independently used for one-semester courses in either of these subjects. The main ideas are illustrated and further developed by numerous examples and over 300 exercises. Detailed solutions are provided for many of these exercises, making An Introduction to Riemannian Geometry ideal for self-study.
The Laplacian on a Riemannian Manifold
Author: Steven Rosenberg
Publisher: Cambridge University Press
Published: 1997-01-09
Total Pages: 190
ISBN-13: 9780521468312
DOWNLOAD EBOOKThis text on analysis of Riemannian manifolds is aimed at students who have had a first course in differentiable manifolds.
Riemannian Geometry in an Orthogonal Frame
Author: Elie Cartan
Publisher: World Scientific
Published: 2001
Total Pages: 284
ISBN-13: 9789810247478
DOWNLOAD EBOOKElie Cartan's book Geometry of Riemannian Manifolds (1928) was one of the best introductions to his methods. It was based on lectures given by the author at the Sorbonne in the academic year 1925-26. A modernized and extensively augmented edition appeared in 1946 (2nd printing, 1951, and 3rd printing, 1988). Cartan's lectures in 1926-27 were different -- he introduced exterior forms at the very beginning and used extensively orthonormal frames throughout to investigate the geometry of Riemannian manifolds. In this course he solved a series of problems in Euclidean and non-Euclidean spaces, as well as a series of variational problems on geodesics. The lectures were translated into Russian in the book Riemannian Geometry in an Orthogonal Frame (1960). This book has many innovations, such as the notion of intrinsic normal differentiation and the Gaussian torsion of a submanifold in a Euclidean multidimensional space or in a space of constant curvature, an affine connection defined in a normal fiber bundle of a submanifold, etc. The only book of Elie Cartan that was not available in English, it has now been translated into English by Vladislav V Goldberg, the editor of the Russian edition.
