Overview
- 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
Part of the book series: Springer Monographs in Mathematics (SMM)
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Table of contents (7 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Reviews
“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)
Authors and Affiliations
About the authors
V.N. Berestovskii (PhD (1979) and DrScD (1990)) was a student at Novosibirsk State University (1966--1975). He was Senior Lecturer and then Full Professor at Omsk State University (1975—2001). From 2001 to the present he has been Leading Researcher at the Sobolev Institute of Mathematics SB RAS. He is the author of 95 papers and 2 monographs.
Yu. G. Nikonorov (PhD (1995) and DrScD (2004)) was a student at Novosibirsk State University (1987--1993). He was Assistant Professor and then Full Professor at the Rubtsovsk Industrial Institute (1996--2009), and Pro Vice-Chancellor (Research) at the Volgodonsk Institute of Service (2009--2010). From 2011 to the present he has been Principal Researcher at the Southern Mathematical Institute of VSC RAS. He is the author of 75 papers and 3 monographs.
Bibliographic Information
Book Title: Riemannian Manifolds and Homogeneous Geodesics
Authors: Valerii Berestovskii, Yurii Nikonorov
Series Title: Springer Monographs in Mathematics
DOI: https://doi.org/10.1007/978-3-030-56658-6
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2020
Hardcover ISBN: 978-3-030-56657-9Published: 06 November 2020
Softcover ISBN: 978-3-030-56660-9Published: 07 November 2021
eBook ISBN: 978-3-030-56658-6Published: 05 November 2020
Series ISSN: 1439-7382
Series E-ISSN: 2196-9922
Edition Number: 1
Number of Pages: XXII, 482
Number of Illustrations: 1 b/w illustrations
Topics: Differential Geometry, Topological Groups, Lie Groups, Convex and Discrete Geometry, Non-associative Rings and Algebras