On a class of weakly Einstein Finsler metrics
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- Shen, Z. & Yang, G. Isr. J. Math. (2014) 199: 773. doi:10.1007/s11856-013-0060-5
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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.