Riemannian Manifolds and Homogeneous Geodesics

Valerii Berestovskii, Yurii Nikonorov

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English

Springer Nature Switzerland AG
07 November 2021

Discrete mathematics; Algebra; Groups & group theory; Geometry; Differential & Riemannian geometry

Series: Springer Monographs in Mathematics

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.

By: Valerii Berestovskii, Yurii Nikonorov
Imprint: Springer Nature Switzerland AG
Country of Publication: Switzerland
Edition: 2020 ed.
Dimensions: Height: 235mm, Width: 155mm,
Weight: 765g
ISBN: 9783030566609
ISBN 10: 3030566609
Series: Springer Monographs in Mathematics
Pages: 482
Publication Date: 07 November 2021
Audience: College/higher education , Further / Higher Education
Format: Paperback
Publisher's Status: Active

Introduction. - 1 Riemannian Manifolds. - 2 Lie Groups and Lie Algebras. - 3 Isometric Flows and Killing Vector Fields on Riemannian Manifolds. - 4 Homogeneous Riemannian Manifolds. - 5 Manifolds With Homogeneous Geodesics. - 6 Generalized Normal Homogeneous ManifoldsWith Intrinsic Metrics. - 7 Clifford–Wolf Homogeneous Riemannian Manifolds. - References. - List of Tables. - Index.

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.

Reviews for 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)