Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 33, No. 2, pp. 373-385 (2017)

Einstein Metrics on Warped Product Finsler Spaces

M. Khameforoush Yazdi, Y. Alipour Fakhri and M. M. Rezaii

Payame Noor University and Amirkabir University of Technology

Abstract: In this paper, we prove that a warped product Finsler metric is an Einstein metric if and only if some partial differential equations are satisfied. Several results are obtained in special cases, for example, the case of Riemannian, Locally Minkowski, and Berwald spaces. Moreover, we present the static vacuum Einstein equations on Finsler manifold.

Keywords: Finsler space, Warped product, Einstein metric

Classification (MSC2000): 53C60; 53C20, 53C25

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