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Riemannian Manifolds and Homogeneous Geodesics de Valerii Berestovskii

Riemannian Manifolds and Homogeneous Geodesics: Springer Monographs in Mathematics

Autor Valerii Berestovskii, Yurii Nikonorov
en Limba Engleză Paperback – 7 noi 2021
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.


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Specificații

ISBN-13: 9783030566609
ISBN-10: 3030566609
Pagini: 482
Ilustrații: XXII, 482 p. 1 illus.
Dimensiuni: 155 x 235 mm
Greutate: 0.77 kg
Ediția:1st ed. 2020
Editura: Springer International Publishing
Colecția Springer
Seria Springer Monographs in Mathematics

Locul publicării:Cham, Switzerland

Cuprins

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. 


Recenzii

“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)

Notă biografică

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.

Textul de pe ultima copertă

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.


Caracteristici

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