English

On projectively flat Kropina metrics

Differential Geometry 2013-04-10 v2

Abstract

In this paper, a characteristic condition of the projectively flat Kropina metric is given. By it, we prove that a Kropina metric F=α2/βF=\alpha^2/\beta with constant curvature KK and βα=1\|\beta\|_{\alpha}=1 is projectively flat if and only if FF is locally Minkowskian.

Cite

@article{arxiv.1304.1612,
  title  = {On projectively flat Kropina metrics},
  author = {Xiaoling Zhang and Yibing Shen},
  journal= {arXiv preprint arXiv:1304.1612},
  year   = {2013}
}

Comments

This paper has been withdrawn by the author due to a crucial improvement

R2 v1 2026-06-21T23:54:22.669Z