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.
Rezensionen / Stimmen
"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)
Produkt-Info
Reihe
Auflage
Sprache
Verlagsort
Verlagsgruppe
Springer International Publishing
Zielgruppe
Für höhere Schule und Studium
Illustrationen
1
1 s/w Abbildung
1 Illustrations, black and white; XXII, 482 p. 1 illus.
Maße
Höhe: 235 mm
Breite: 155 mm
Dicke: 28 mm
Gewicht
ISBN-13
978-3-030-56660-9 (9783030566609)
DOI
10.1007/978-3-030-56658-6
Schweitzer Klassifikation
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.
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.
