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Springer Monographs in Mathematics

Homogeneous Finsler Spaces

Authors: Deng, Shaoqiang

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  • Presents the most recent results on the applications of Lie theory to Finsler geometry
  • Provides an accessible introduction to Finsler geometry that allows the reader to quickly understand topics and to access related problems
  • Contains related work concerning Randers spaces, making it suitable for readers with a background in biology, as well as various topics for readers with backgrounds in pure algebra​
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About this book

Homogeneous Finsler Spaces is the first book to emphasize the relationship between Lie groups and Finsler geometry, and the first to show the validity in using Lie theory for the study of Finsler geometry problems. This book contains a series of new results obtained by the author and collaborators during the last decade. The topic of Finsler geometry has developed rapidly in recent years. One of the main reasons for its surge in development is its use in many scientific fields, such as general relativity, mathematical biology, and phycology (study of algae).  This monograph introduces the most recent developments in the study of Lie groups and homogeneous Finsler spaces,  leading the reader to directions for further development. The book contains many interesting results such as a Finslerian version of  the Myers-Steenrod Theorem, the existence theorem for invariant non-Riemannian Finsler metrics on coset spaces, the Berwaldian characterization of globally symmetric Finsler spaces, the construction of examples of reversible non-Berwaldian Finsler spaces with vanishing S-curvature, and a classification of homogeneous Randers spaces with isotropic S-curvature and positive flag curvature. Readers with some background in Lie theory or differential geometry can quickly begin studying problems concerning Lie groups and Finsler geometry.​

Reviews

From the reviews:

“The main purpose of this book is to show how ideas from Lie theory have spread to Finsler geometry. This book is the first one in the field of homogeneous Finsler spaces. … Finsler geometry has been developing rapidly, but this book may give a new spirit to Finsler geometry from the view of Lie theory, and it can be highly recommended to anyone who wants to study Finsler geometry from this point of view.” (Hamid Reza Salimi Moghaddam, Mathematical Reviews, June, 2013)

“The aim of the present book is to introduce the aspects of Finsler geometry that can be expressed in terms of Lie theory, having as permanent example the case of homogeneous/symmetric Riemannian manifolds. In this way, new very interesting facts are produced by non-Riemannian tools and geometrical objects like flag and S-curvature. … this book will be of great interest for a large number of geometers.” (Radu Miron, Zentralblatt MATH, Vol. 1253, 2013)


Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook $109.00
price for USA in USD
  • ISBN 978-1-4614-4244-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.99
price for USA in USD
  • ISBN 978-1-4614-4243-1
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
Softcover $139.00
price for USA in USD
  • ISBN 978-1-4899-9476-9
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Homogeneous Finsler Spaces
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2012
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4614-4244-8
DOI
10.1007/978-1-4614-4244-8
Hardcover ISBN
978-1-4614-4243-1
Softcover ISBN
978-1-4899-9476-9
Series ISSN
1439-7382
Edition Number
1
Number of Pages
XIV, 242
Topics

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