On the Finsler Geometry of Four-Dimensional Einstein Lie Groups

On the Finsler Geometry of Four-Dimensional Einstein Lie Groups In this paper, we study left invariant ða; bÞ-metrics on four-dimensional real Lie groups equipped with left invariant Einstein Riemannian metrics. We classify all left invariant ða; bÞ-metrics of Berwald type induced by a left invariant Einstein Riemannian metric and a left invariant vector field and show that all of them are locally Minkowskian. All left invariant Randers metrics of Douglas type, and all Einstein Kropina metrics induced by a left invariant Riemannian metric and a left invariant vector field, are classified. Finally, the flag curvatures of these spaces are investigated and in a special case the geodesics are computed. Keywords Flag curvature  Lie group  (a, b)-metric  Douglas spaces Mathematics Subject Classification 53C30  53C60  22E60 1 Introduction In this article we study left invariant ða; bÞ-metrics of Berwald type, left invariant Randers metrics of Douglas Among Finsler metrics, ða; bÞ-metrics are very interesting, type and the classification of left invariant Einstein Kropina since they are computable and have many applications. For metrics on four-dimensional Lie groups equipped with left example, Randers metric, which is a special type of ða; bÞ- invariant Einstein Riemannian metrics. metrics, has been introduced because of its applications in Here, http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Iranian Journal of Science and Technology, Transactions A: Science Springer Journals

On the Finsler Geometry of Four-Dimensional Einstein Lie Groups

Loading next page...
 
/lp/springer_journal/on-the-finsler-geometry-of-four-dimensional-einstein-lie-groups-rMpgY9iFE7
Publisher
Springer International Publishing
Copyright
Copyright © 2018 by Shiraz University
Subject
Engineering; Engineering, general; Chemistry/Food Science, general; Earth Sciences, general; Life Sciences, general; Materials Science, general; Physics, general
ISSN
1028-6276
eISSN
2364-1819
D.O.I.
10.1007/s40995-018-0583-z
Publisher site
See Article on Publisher Site

Abstract

In this paper, we study left invariant ða; bÞ-metrics on four-dimensional real Lie groups equipped with left invariant Einstein Riemannian metrics. We classify all left invariant ða; bÞ-metrics of Berwald type induced by a left invariant Einstein Riemannian metric and a left invariant vector field and show that all of them are locally Minkowskian. All left invariant Randers metrics of Douglas type, and all Einstein Kropina metrics induced by a left invariant Riemannian metric and a left invariant vector field, are classified. Finally, the flag curvatures of these spaces are investigated and in a special case the geodesics are computed. Keywords Flag curvature  Lie group  (a, b)-metric  Douglas spaces Mathematics Subject Classification 53C30  53C60  22E60 1 Introduction In this article we study left invariant ða; bÞ-metrics of Berwald type, left invariant Randers metrics of Douglas Among Finsler metrics, ða; bÞ-metrics are very interesting, type and the classification of left invariant Einstein Kropina since they are computable and have many applications. For metrics on four-dimensional Lie groups equipped with left example, Randers metric, which is a special type of ða; bÞ- invariant Einstein Riemannian metrics. metrics, has been introduced because of its applications in Here,

Journal

Iranian Journal of Science and Technology, Transactions A: ScienceSpringer Journals

Published: Jun 4, 2018

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off