Riemannian Manifolds and Homogeneous Geodesics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Riemannian Manifolds and Homogeneous Geodesics write by Valerii Berestovskii. This book was released on 2020-11-05. Riemannian Manifolds and Homogeneous Geodesics available in PDF, EPUB and Kindle. This book is devoted to Killing vector fields and the one-parameter isometry groups of Riemannian manifolds generated by them. It also provides a detailed introduction to homogeneous geodesics, that is, geodesics that are integral curves of Killing vector fields, presenting both classical and modern results, some very recent, many of which are due to the authors. The main focus is on the class of Riemannian manifolds with homogeneous geodesics and on some of its important subclasses. To keep the exposition self-contained the book also includes useful general results not only on geodesic orbit manifolds, but also on smooth and Riemannian manifolds, Lie groups and Lie algebras, homogeneous Riemannian manifolds, and compact homogeneous Riemannian spaces. The intended audience is graduate students and researchers whose work involves differential geometry and transformation groups.
Topics in Geometry
Topics in Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Topics in Geometry write by Simon Gindikin. This book was released on 1996-06-27. Topics in Geometry available in PDF, EPUB and Kindle. This collection of articles serves to commemorate the legacy of Joseph D'Atri, who passed away on April 29, 1993, a few days after his 55th birthday. Joe D' Atri is credited with several fundamental discoveries in ge ometry. In the beginning of his mathematical career, Joe was interested in the generalization of symmetrical spaces in the E. Cart an sense. Symmetric spaces, differentiated from other homogeneous manifolds by their geomet rical richness, allows the development of a deep analysis. Geometers have been constantly interested and challenged by the problem of extending the class of symmetric spaces so as to preserve their geometrical and analytical abundance. The name of D'Atri is tied to one of the most successful gen eralizations: Riemann manifolds in which (local) geodesic symmetries are volume-preserving (up to sign). In time, it turned out that the majority of interesting generalizations of symmetrical spaces are D'Atri spaces: natu ral reductive homogeneous spaces, Riemann manifolds whose geodesics are orbits of one-parameter subgroups, etc. The central place in D'Atri's research is occupied by homogeneous bounded domains in en, which are not symmetric. Such domains were discovered by Piatetskii-Shapiro in 1959, and given Joe's strong interest in the generalization of symmetric spaces, it was very natural for him to direct his research along this path.
Riemannian Manifolds
Riemannian Manifolds - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Riemannian Manifolds write by John M. Lee. This book was released on 2006-04-06. Riemannian Manifolds available in PDF, EPUB and Kindle. 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.
Introduction to Riemannian Manifolds
Introduction to Riemannian Manifolds - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to Riemannian Manifolds write by John M. Lee. This book was released on 2019-01-02. Introduction to Riemannian Manifolds available in PDF, EPUB and Kindle. 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.
The Geometry of Curvature Homogeneous Pseudo-Riemannian Manifolds
The Geometry of Curvature Homogeneous Pseudo-Riemannian Manifolds - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Geometry of Curvature Homogeneous Pseudo-Riemannian Manifolds write by Peter B. Gilkey. This book was released on 2007. The Geometry of Curvature Homogeneous Pseudo-Riemannian Manifolds available in PDF, EPUB and Kindle. Pseudo-Riemannian geometry is an active research field not only in differential geometry but also in mathematical physics where the higher signature geometries play a role in brane theory. An essential reference tool for research mathematicians and physicists, this book also serves as a useful introduction to students entering this active and rapidly growing field. The author presents a comprehensive treatment of several aspects of pseudo-Riemannian geometry, including the spectral geometry of the curvature tensor, curvature homogeneity, and StanilovOCoTsankovOCoVidev theory."
