Riemannian Manifolds and Homogeneous Geodesics
Buch in deiner Nähe kaufen
Beschreibung
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.
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.
Provides a detailed presentation of the foundations of Riemannian geometry and the theory of isometric flows on Riemannian manifolds Gives a self-contained general introduction to the theory of homogeneous Riemannian spaces, with many illustrative examples Includes numerous results, some very recent, on geodesic orbit Riemannian spaces and their important subclasses
Autor*in
Valerii Berestovskii
Themen in »Riemannian Manifolds and Homogeneous Geodesics«
Geodesic orbit spaces Generalized normal homogeneous spaces Homogeneous spaces Geodesics Riemannian manifolds
Stimmen zu »Riemannian Manifolds and Homogeneous Geodesics«
“The book by V. Berestovskii and Y. Nikonorov is a welcome contribution in homogeneous geometry, which can be appreciated by a wide range of audience, from graduate students to focused researchers.” (Andreas Arvanitoyeorgos, zbMATH 1460.53001, 2021)
()