Douglas (α,β)-metrics on four-dimensional nilpotent Lie groups

Document Type : Original Article

Authors

1 Department of Pure Mathematics, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan, 81746-73441-Iran. Email: salimi.moghaddam@gmail.com

2 Department of Mathematics, Isfahan University of Technology, Isfahan, 84156-83111-Iran. Email:hossein.abedikarimi@gmail.com

3 Faculty of Basic Sciences, University of Shahreza, P. O. Box: 86149- 56841, Shahreza, Iran. Email: nasehi.mehri@gmail.com

Abstract

In this paper, we give a classification of left-invariant Douglas and Berwald (α,β)-metrics on simply connected four-dimensional nilpotent Lie groups. We show that there are not any bi-invariant Randers metrics on four-dimensional nilpotent Lie groups. Then, we explicitly give the flag curvature formulas and geodesic vectors of these spaces. Finally, we give the formula of S-curvature of left-invariant Randers metrics of Douglas type.

Keywords

Journal of Finsler Geometry and its Applications
Volume 1, Issue 2
December 2020
Pages 15-26

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