Riemannian Manifolds and Homogeneous Geode...

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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.

Über den Autor

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.

Zusammenfassung

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

Inhaltsverzeichnis

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 Manifolds

With Intrinsic Metrics. - 7 Clifford-Wolf Homogeneous Riemannian Manifolds. - References. - List of Tables. - Index.

Details

Erscheinungsjahr:	2021
Fachbereich:	Geometrie
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Springer Monographs in Mathematics
Inhalt:	xxii 482 S. 1 s/w Illustr. 482 p. 1 illus.
ISBN-13:	9783030566609
ISBN-10:	3030566609
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Berestovskii, Valerii Nikonorov, Yurii
Hersteller:	Springer Palgrave Macmillan Springer International Publishing AG Springer Monographs in Mathematics
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 28 mm
Von/Mit:	Valerii Berestovskii (u. a.)
Erscheinungsdatum:	07.11.2021
Gewicht:	0,756 kg