On a class of weakly Einstein Finsler metrics
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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.
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- D. Bao and C. Robles, Ricci and flag curvatures in Finsler geometry, in A sampler of Reimann-Finsler Geometry, Mathematical Sciences Research Institute Publications, Vol. 50, Cambridge University Press, Cambridge, 2005, pp. 197–259.Google Scholar
- B. Chen, Z. Shen and L. Zhao, On a calss of Ricci flat Finsler metrics in Finsler geometry, Journal of Geometry and Physics, preprint.Google Scholar
- Z. Shen and G. Yang, On square metrics of scalar flag curvature, preprint.Google Scholar
- Z. Shen and G. C. Yildirim, A characterization of Randers metrics of scalar flag curvature, in Survey in Geometric Analysis and Relativity, Advanced Lectures in Mathematics, Vol. 23, International Press, Somerville, MA 2012, pp. 345–358.Google Scholar
- Q. Xia, On Kropina metrics of weakly isotropic flag curvature, preprint.Google Scholar
- G. Yang, On a class of two-dimensional singular Douglas and projectively flat Finsler metrics, preprint.Google Scholar
- G. Yang, On a class of singular Douglas and projectively flat Finsler metrics, preprint.Google Scholar
- G. Yang, On a class of singular projectively flat Finsler metrics with constant flag curvature, preprint.Google Scholar
- R. Yoshikawa and K. Okubo, Kropina spaces of constant curvature II, arXiv: math/1110.5128v1 [math.DG] 24 Oct 2011.Google Scholar
- X. Zhang and Y. Shen, On Einstein Kropina metrics, Deffernetial Geometry and its Application, to appear.Google Scholar