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Homogeneous Structures on Riemannian Manifolds

1983-06-23 Mathematics
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Release : 1983-06-23
Genre : Mathematics
Kind : eBook
Book Rating : 893/5 ( reviews)

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Book Synopsis Homogeneous Structures on Riemannian Manifolds by : F. Tricerri

Download or read book Homogeneous Structures on Riemannian Manifolds written by F. Tricerri. This book was released on 1983-06-23. Available in PDF, EPUB and Kindle. Book excerpt: The central theme of this book is the theorem of Ambrose and Singer, which gives for a connected, complete and simply connected Riemannian manifold a necessary and sufficient condition for it to be homogeneous. This is a local condition which has to be satisfied at all points, and in this way it is a generalization of E. Cartan's method for symmetric spaces. The main aim of the authors is to use this theorem and representation theory to give a classification of homogeneous Riemannian structures on a manifold. There are eight classes, and some of these are discussed in detail. Using the constructive proof of Ambrose and Singer many examples are discussed with special attention to the natural correspondence between the homogeneous structure and the groups acting transitively and effectively as isometrics on the manifold.

Homogeneous Structures on Riemannian Manifolds

2014-05-14 MATHEMATICS
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Release : 2014-05-14
Genre : MATHEMATICS
Kind : eBook
Book Rating : 309/5 ( reviews)

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Book Synopsis Homogeneous Structures on Riemannian Manifolds by : Franco Tricerri

Download or read book Homogeneous Structures on Riemannian Manifolds written by Franco Tricerri. This book was released on 2014-05-14. Available in PDF, EPUB and Kindle. Book excerpt: The central theme of this book is the theorem of Ambrose and Singer, which gives for a connected, complete and simply connected Riemannian manifold a necessary and sufficient condition for it to be homogeneous. This is a local condition which has to be satisfied at all points, and in this way it is a generalization of E. Cartan's method for symmetric spaces. The main aim of the authors is to use this theorem and representation theory to give a classification of homogeneous Riemannian structures on a manifold. There are eight classes, and some of these are discussed in detail. Using the constructive proof of Ambrose and Singer many examples are discussed with special attention to the natural correspondence between the homogeneous structure and the groups acting transitively and effectively as isometrics on the manifold.

Homogeneous Structures on Riemannian Manifolds

1983-06-23 Mathematics
Download Homogeneous Structures on Riemannian Manifolds PDF Online Free

Author :
Release : 1983-06-23
Genre : Mathematics
Kind : eBook
Book Rating : 890/5 ( reviews)

GET EBOOK


Book Synopsis Homogeneous Structures on Riemannian Manifolds by : F. Tricerri

Download or read book Homogeneous Structures on Riemannian Manifolds written by F. Tricerri. This book was released on 1983-06-23. Available in PDF, EPUB and Kindle. Book excerpt: The central theme of this book is the theorem of Ambrose and Singer, which gives for a connected, complete and simply connected Riemannian manifold a necessary and sufficient condition for it to be homogeneous. This is a local condition which has to be satisfied at all points, and in this way it is a generalization of E. Cartan's method for symmetric spaces. The main aim of the authors is to use this theorem and representation theory to give a classification of homogeneous Riemannian structures on a manifold. There are eight classes, and some of these are discussed in detail. Using the constructive proof of Ambrose and Singer many examples are discussed with special attention to the natural correspondence between the homogeneous structure and the groups acting transitively and effectively as isometrics on the manifold.

Pseudo-Riemannian Homogeneous Structures

2019-08-14 Mathematics
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Release : 2019-08-14
Genre : Mathematics
Kind : eBook
Book Rating : 529/5 ( reviews)

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Book Synopsis Pseudo-Riemannian Homogeneous Structures by : Giovanni Calvaruso

Download or read book Pseudo-Riemannian Homogeneous Structures written by Giovanni Calvaruso. This book was released on 2019-08-14. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an up-to-date presentation of homogeneous pseudo-Riemannian structures, an essential tool in the study of pseudo-Riemannian homogeneous spaces. Benefiting from large symmetry groups, these spaces are of high interest in Geometry and Theoretical Physics. Since the seminal book by Tricerri and Vanhecke, the theory of homogeneous structures has been considerably developed and many applications have been found. The present work covers a gap in the literature of more than 35 years, presenting the latest contributions to the field in a modern geometric approach, with special focus on manifolds equipped with pseudo-Riemannian metrics. This unique reference on the topic will be of interest to researchers working in areas of mathematics where homogeneous spaces play an important role, such as Differential Geometry, Global Analysis, General Relativity, and Particle Physics.

Riemannian Manifolds and Homogeneous Geodesics

2020-11-05 Mathematics
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Release : 2020-11-05
Genre : Mathematics
Kind : eBook
Book Rating : 587/5 ( reviews)

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Book Synopsis Riemannian Manifolds and Homogeneous Geodesics by : Valerii Berestovskii

Download or read book Riemannian Manifolds and Homogeneous Geodesics written by Valerii Berestovskii. This book was released on 2020-11-05. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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