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Springer Monographs in Mathematics

Riemannian Manifolds and Homogeneous Geodesics

Authors: Berestovskii, Valerii, Nikonorov, Yurii

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  • 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
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eBook $109.00
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  • ISBN 978-3-030-56658-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.99
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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.


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.


Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook $109.00
price for Mexico
  • ISBN 978-3-030-56658-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.99
price for Mexico
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Bibliographic Information

Bibliographic Information
Book Title
Riemannian Manifolds and Homogeneous Geodesics
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2020
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-56658-6
DOI
10.1007/978-3-030-56658-6
Hardcover ISBN
978-3-030-56657-9
Series ISSN
1439-7382
Edition Number
1
Number of Pages
XXII, 482
Number of Illustrations
1 b/w illustrations
Topics