ON LOCALLY DUALLY FLAT FINSLER METRICS-Reference-Cited by-同舟云学术

ON LOCALLY DUALLY FLAT FINSLER METRICS

Published:2010-11 Issue:11 Volume:21 Page:1531-1543
ISSN:0129-167X
Container-title:International Journal of Mathematics
language:en
Short-container-title:Int. J. Math.

Author:

CHENG XINYUE¹,SHEN ZHONGMIN²,ZHOU YUSHENG³

Affiliation:

1. School of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, P. R. China

2. Department of Mathematical Sciences, Indiana University Purdue University Indianapolis (IUPUI), Indianapolis, IN 46202-3216, USA

3. Department of Mathematics, Guiyang University, Guiyang 550005, P. R. China

Abstract

Locally dually flat Finsler metrics arise from information geometry. Such metrics have special geometric properties. In this paper, we characterize locally dually flat and projectively flat Finsler metrics and study a special class of Finsler metrics called Randers metrics which are expressed as the sum of a Riemannian metric and a one-form. We find some equations that characterize locally dually flat Randers metrics and classify those with isotropic S-curvature.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0129167X10006616

Reference14 articles.

1. Differential-Geometrical Methods in Statistics

2. AMS Translation of Math. Monographs;Amari S.-I.,2000

3. On Randers spaces of constant flag curvature

4. S. Bácsó, X. Cheng and Z. Shen, Curvature Properties of (α, β)-Metrics, Adv. Stud. Pure Math. 48 (Math. Soc. of Japan, 2007) pp. 73–110.

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