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In this work, we consider a class of Finsler metrics using the warped product notion introduced by Chen, S. and Zhao (2018), with another warping, one that is consistent with static spacetimes. We will give the PDE characterization for the proposed metrics to be Ricci-flat and explicitly construct two non-Riemannian examples.
In this paper we study warped product Finsler metrics and show that the notion of isotropic $E$-curvature and isotropic $S$-curvature are equivalent for this class of metrics.
In this paper we have studied the class of Finsler metrics, called C3-like metrics which satisfy the un-normal and normal Ricci flow equation and proved that such metrics are Einstein.
We introduce a combinatorial method to construct indefinite Ricci-flat metrics on nice nilpotent Lie groups. We prove that every nilpotent Lie group of dimension $leq6$, every nice nilpotent Lie group of dimension $leq7$ and every two-step nilpoten
An $(alpha,beta)$-manifold $(M,F)$ is a Finsler manifold with the Finsler metric $F$ being defined by a Riemannian metric $alpha$ and $1$-form $beta$ on the manifold $M$. In this paper, we classify $n$-dimensional $(alpha,beta)$-manifolds (non-Rander
We prove a uniform diameter bound for long time solutions of the normalized Kahler-Ricci flow on an $n$-dimensional projective manifold $X$ with semi-ample canonical bundle under the assumption that the Ricci curvature is uniformly bounded for all ti