Einstein Finslerian Space with Special (α , β )-Metric

Pradeep Kumar*1, Madhu T S1 and Chandru K2

1Department of Mathematics, Acharya Institute of Technology, Soladevanahalli, Bengaluru-560107, Karnataka, INDIA. 2Department of Mathematics, PESITM, Shivamogga, Karnataka, INDIA.


Einstein-Finslerian metrics are solutions to Einstein eld equation in General Relativity containing Ricci-flat metrics. In this paper, we have determined the Riemann curvature of special (α , β )-metric 𝐿 = 𝜇1𝛼 + 𝜇2𝛽 + 𝜇3 𝛽2 𝛼 ; where μ1 , μ 2 and μ 3 are constants. Then we have obtained the necessary and sufficient condition for that (α , β )-metric to be Einstein metric, when β is a constant killing form. Finally, we have proved that the mentioned Einstein metric is Ricci flat. MSC: 53B20, 53B40, 53C60.

Keywords :(α , β )-metrics, Riemannian curvature, Ricci curvature, Einstein Finsler space.

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