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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.

Riemannian Manifolds with Homogeneous Geodesics

1991 Geodesics (Mathematics)
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Release : 1991
Genre : Geodesics (Mathematics)
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Book Synopsis Riemannian Manifolds with Homogeneous Geodesics by : Oldřich Kowalski

Download or read book Riemannian Manifolds with Homogeneous Geodesics written by Oldřich Kowalski. This book was released on 1991. Available in PDF, EPUB and Kindle. Book excerpt:

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 Geodesics in Homogeneous Riemannian Manifolds - Examples

2000
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Release : 2000
Genre :
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Book Synopsis Homogeneous Geodesics in Homogeneous Riemannian Manifolds - Examples by : Oldřich Kowalski

Download or read book Homogeneous Geodesics in Homogeneous Riemannian Manifolds - Examples written by Oldřich Kowalski. This book was released on 2000. Available in PDF, EPUB and Kindle. Book excerpt:

Topics in Geometry

1996-06-27 Mathematics
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Release : 1996-06-27
Genre : Mathematics
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Book Rating : 283/5 ( reviews)

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Book Synopsis Topics in Geometry by : Simon Gindikin

Download or read book Topics in Geometry written by Simon Gindikin. This book was released on 1996-06-27. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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