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 EBOOK →Book 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 EBOOK →This 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.
Geometry of Manifolds
Author: K. Shiohama
Publisher: Elsevier
Published: 1989-10-04
Total Pages: 517
ISBN-13: 0080925782
DOWNLOAD EBOOK →This volume contains the papers presented at a symposium on differential geometry at Shinshu University in July of 1988. Carefully reviewed by a panel of experts, the papers pertain to the following areas of research: dynamical systems, geometry of submanifolds and tensor geometry, lie sphere geometry, Riemannian geometry, Yang-Mills Connections, and geometry of the Laplace operator.
Contact manifolds in Riemannian geometry
On the Hypotheses Which Lie at the Bases of Geometry
Author: Bernhard Riemann
Publisher: Birkhäuser
Published: 2016-04-19
Total Pages: 172
ISBN-13: 3319260421
DOWNLOAD EBOOK →This 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.
First Steps in Differential Geometry
Author: Andrew McInerney
Publisher: Springer Science & Business Media
Published: 2013-07-09
Total Pages: 420
ISBN-13: 1461477328
DOWNLOAD EBOOK →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.
Introduction to Riemannian Manifolds
Author: John M. Lee
Publisher: Springer
Published: 2019-01-02
Total Pages: 437
ISBN-13: 3319917552
DOWNLOAD EBOOK →This 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.
Handbook of Pseudo-Riemannian Geometry and Supersymmetry
Author: Vicente Cortés
Publisher: European Mathematical Society
Published: 2010
Total Pages: 972
ISBN-13: 9783037190791
DOWNLOAD EBOOK →The purpose of this handbook is to give an overview of some recent developments in differential geometry related to supersymmetric field theories. The main themes covered are: Special geometry and supersymmetry Generalized geometry Geometries with torsion Para-geometries Holonomy theory Symmetric spaces and spaces of constant curvature Conformal geometry Wave equations on Lorentzian manifolds D-branes and K-theory The intended audience consists of advanced students and researchers working in differential geometry, string theory, and related areas. The emphasis is on geometrical structures occurring on target spaces of supersymmetric field theories. Some of these structures can be fully described in the classical framework of pseudo-Riemannian geometry. Others lead to new concepts relating various fields of research, such as special Kahler geometry or generalized geometry.
An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised
Author: William Munger Boothby
Publisher: Gulf Professional Publishing
Published: 2003
Total Pages: 444
ISBN-13: 9780121160517
DOWNLOAD EBOOK →The second edition of An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised has sold over 6,000 copies since publication in 1986 and this revision will make it even more useful. This is the only book available that is approachable by "beginners" in this subject. It has become an essential introduction to the subject for mathematics students, engineers, physicists, and economists who need to learn how to apply these vital methods. It is also the only book that thoroughly reviews certain areas of advanced calculus that are necessary to understand the subject. Line and surface integrals Divergence and curl of vector fields
