Ricci Tensor of a Finsler space with special $(alpha,eta)$-metrics

Acta Mathematica Academiae Paedagogicae Nyíregyháziensis

Narasimhamurthy Senajji Kampalappa¹  Roopa Mallappa Kariyappa¹ 

[1] Kuvempu University

关键词: Ricci curvature;   

DOI  :  

学科分类：数学（综合）

来源: Academia Paedagogica Nyiregyhaziensis. Acta Mathematica

【 摘 要 】

In this paper, we investigate the Ricci tensor of a Finsler space of a special $(alpha, eta)$-metric $F=frac{(alpha+eta)^{2}}{alpha}+eta$, where $alpha=sqrt{a_{ij}y^{i}y^{j}}$ be a Riemannian metric and $eta$ be a 1-form. We also prove that if $alpha$ is a positive (negative) sectional curvature and $F$ is of $alpha$-parallel Ricci curvature with constant Killing 1-form $eta$, then $(M, F)$ is a Riemannian Einstein space.

【 授权许可】

Unknown