Related papers: Finslerian metrics locally conformally $R$-Einstei…
Recently the present authors introduced a general class of Finsler connections which leads to a smart representation of connection theory in Finsler geometry and yields to a classification of Finsler connections into the three classes. Here…
In this paper, we explore the similarity between normal homogeneity and $\delta$-homogeneity in Finsler geometry. They are both non-negatively curved Finsler spaces. We show that any connected $\delta$-homogeneous Finsler space is…
Isotropic almost complex structures induce a class of Riemannian metrics on tangent bundle of a Riemannian manifold. In this paper the curvature tensors of these metrics will be calculated.
In Lorentz-Finsler geometry it is natural to define the Finsler Lagrangian over a cone (Asanov's approach) or over the whole slit tangent bundle (Beem's approach). In the former case one might want to add differentiability conditions at the…
In this paper, I shall demonstrate that sufficiently high-dimensional closed positively-curved Riemannian manifolds are either diffeomorphic to a spherical space form, or isometric to a locally compact rank one symmetric space. This…
In this article, we define the Chern-Robinson connection on the complexify tangent bundle of an almost Robinson manifold and we study the curvature associated to. Various Bianchi identities are obtained together with an application to…
Some links between Lorentz and Finsler geometries have been developed in the last years, with applications even to the Riemannian case. Our purpose is to give a brief description of them, which may serve as an introduction to recent…
We calculate curvature tensors of metrics on the total spaces of holomorphic fibrations. Our main tool is a theory of Chern connections and curvature forms for possibly degenerate Hermitian forms on holomorphic vector bundles. We prove a…
The $\Gamma$-limit for a sequence of length functionals associated with a one parameter family of Riemannian manifolds is computed analytically. The Riemannian manifold is of `two-phase' type, that is, the metric coefficient takes values in…
We obtain some results in both Lorentz and Finsler geometries, by using a correspondence between the conformal structure (Causality) of standard stationary spacetimes on $M=\R\times S$ and Randers metrics on $S$. In particular, for…
The main facts of the geometry of Finslerian 4-spinors are formulated. It is shown that twistors are a special case of Finslerian 4-spinors. The close connection between Finslerian 4-spinors and the geometry of a 16-dimensional vector…
On a smooth connected manifold, we consider all possible locally elliptic and locally bounded measurable coefficient Riemannian metrics called rough Riemannian metrics. We equip this set with an extended metric which is connected if and…
We extend Tsuji's iterative construction of complete K\"ahler--Einstein metrics with negative scalar curvature to noncompact K\"ahler manifolds with bounded geometry, using Berndtsson's method from the compact setting. Consequently, given a…
The aim of the present paper is to provide a global presentation of the theory of special Finsler manifolds. We introduce and investigate globally (or intrinsically, free from local coordinates) many of the most important and most commonly…
Cone spherical metrics are conformal metrics with constant curvature one and finitely many conical singularities on compact Riemann surfaces. A cone spherical metric is called irreducible if each developing map of the metric does not have…
A Finsler space $(M,F)$ is called flag-wise positively curved, if for any $x\in M$ and any tangent plane $\mathbf{P}\subset T_xM$, we can find a nonzero vector $y\in \mathbf{P}$, such that the flag curvature $K^F(x,y, \mathbf{P})>0$. Though…
We analyze the foundations of Finsler gravity theories with metric compatible connections constructed on nonholonomic tangent bundles, or (pseudo) Riemannian manifolds. There are considered "minimal" modifications of Einstein gravity…
In this manuscript, we study bounded positive solutions to the Finslerian Allen-Cahn equation. The Allen-Cahn equation is widely applied and connected to many mathematical branches. We find the Finslerian Allen-Cahn equation is also an…
On the product of two Finsler manifolds M1 M2, we consider the twisted metric F which is construct by using Finsler metrics F1 and F2 on the manifolds M1 and M2, respectively. We introduce horizontal and vertical distributions on twisted…
In this paper, we characterize locally dually flat generalized m-th root Finsler metrics. Then we find a condition under which a generalized m-th root metric is projectively related to a m-th root metric. Finally, we prove that if a…