Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 32, No. 1, pp. 165-200 (2016)

Matsumoto metrics of reversible curvature

A. Tayebi and T. Tabatabaeifar

University of Qom and Amirkabir University

Abstract: In this paper, we study the reversibility of Riemann curvature and Ricci curvature for the Matsumoto metric and prove three global results. First, we prove that a Matsumoto metric is R-reversible if and only if it is R-quadratic. Then we show that a Matsumoto metric is Ricci-reversible if and only if it is Ricci-quadratic. Finally, we prove that every weakly Einstein Matsumoto metric is Ricci-reversible.

Keywords: Matsumoto metric, Riemannian curvature, Ricci curvature

Classification (MSC2000): 53C60; 53C25

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