Related papers: On isotropic Berwald scalar curvature

In this paper the projective curvature invariants of a complex Finsler space are obtained. By means of these invariants the notion of complex Douglas space is then defined. A special approach is devoted to obtain the equivalence conditions…

This manuscript investigates the curvature and topological properties of certain $\infty$-Einstein Finsler metrics on Finsler metric measure spaces. By imposing symmetry conditions, we construct a series of special metrics and analyze their…

We study non-reversible Finsler metrics with constant flag curvature 1 on S^2 and show that the geodesic flow of every such metric is conjugate to that of one of Katok's examples, which form a 1-parameter family. In particular, the length…

For Finsler spaces (M,F) endowed with m-th root metrics, we provide necessary and sufficient conditions in which they are projectively flat, or projectively related to Berwald/Riemann spaces. We also give a specific characterization for…

In this paper, we study the relationship between isoparametric hypersurfaces and hypersurfaces with constant principal curvatures in Finsler spaces. We give some examples of isoparametric hypersurfaces with (non)constant principal…

In this paper, we consider the scalar curvature in the distributional sense of \cite{MR3366052} and the scalar curvature lower bound in the $\beta-$weak $(\beta\in(0, \frac{1}{2}))$ sense of \cite{MR4685089} on an asymptotically flat…

We investigate the rigidity problem for the sharp spectral gap on Finsler manifolds of weighted Ricci curvature bound $\text{Ric}_{\infty} \geq K > 0$. Our main results show that if the equality holds, the manifold necessarily admits a…

In this paper, we study the weakly weighted Einstein-Finsler metrics. First, we show that weakly weighted Einstein-Kropina metrics must be of isotropic S-curvature with respect to the Busemann-Hausdorff volume form under a certain condition…

We show how geodesics, Jacobi vector fields and flag curvature of a Finsler metric behave under Zermelo deformation with respect to a Killing vector field. We also show that Zermelo deformation with respect to a Killing vector field of a…

We relate the (non)existence of lower scalar curvature bounds to the existence of certain distance-decreasing maps. We also give a sufficient condition for the existence of a limiting scalar curvature measure in the backward limit of a…

We consider conformal deformations within a class of incomplete Riemannian metrics which generalize conic orbifold singularities by allowing both warping and any compact manifold (not just quotients of the sphere) to be the "link" of the…

Here, an extension of the Obata-Tanno's theorem to Finsler geometry is established and the following rigidity result is obtained; Every complete connected Finsler manifold of positive constant flag curvature is isometrically homeomorphic to…

The validity of functional inequalities on Finsler metric measure manifolds is based on three non-Riemannian quantities, namely, the reversibility, flag curvature and $S$-curvature induced by the measure. Under mild assumptions on the…

This article is an exposition of four loosely related remarks on the geometry of Finsler manifolds with constant positive flag curvature. <p> The first remark is that there is a canonical Kahler structure on the space of geodesics of such a…

We prove a formula involving the scalar curvature of a Riemannian manifold endowed with a distribution in terms of an adapted orthonormal frame for its tangent bundle. Using the formula, we then investigate the effect of collapsing the…

In this paper, we consider a special class of singular Finsler metrics: $m$-Kropina metrics which are defined by a Riemannian metric and a $1$-form. We show that an $m$-Kropina metric ($m\ne -1$) of scalar flag curvature must be locally…

We investigate whether Szabo's metrizability theorem can be extended to Finsler spaces of indefinite signature. For smooth, positive definite Finsler metrics, this important theorem states that, if the metric is of Berwald type (i.e., its…

We consider deformations of the scalar curvature of a partially integrable pseudohermitian manifold, in analogy with the work of Fischer and Marsden on Riemannian manifolds. In particular, we introduce and discuss $R$-singular spaces, give…

We define a symmetry for a Finsler space with Chern connection and investigate its implementation and properties and find a relation between them and flag curvature.

In the present paper, the flag curvature of invariant Randers metrics on homogeneous spaces and Lie groups is studied. We first give an explicit formula for the flag curvature of invariant Randers metrics arising from invariant Riemannian…