Israel Journal of Mathematics

, Volume 199, Issue 2, pp 773-790

First online:

On a class of weakly Einstein Finsler metrics

  • Zhongmin ShenAffiliated withDepartment of Mathematical Sciences, Indiana University-Purdue University Indianapolis (IUPUI)
  • , Guojun YangAffiliated withDepartment of Mathematics, Sichuan University Email author 

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


In this paper we study a special class of Finsler metrics—m-Kropina metrics which are defined by a Riemannian metric and a 1-form. We prove that a weakly Einstein m-Kropina metric must be Einsteinian. Further, we characterize Einstein m-Kropina metrics in very simple conditions under a suitable deformation, and obtain the local structures of m-Kropina metrics which are of constant flag curvature and locally projectively flat with constant flag curvature respectively.