Related papers: On m-th root Finsler metrics

Finsler metrics are direct generalizations of Riemannian metrics such that the quadratic Riemannian indicatrices in the tangent spaces of a manifold are replaced by more general convex bodies as unit spheres. A linear connection on the base…

In this paper, I will show how to use beta-deformations to deal with dual flatness of Randers metrics. beta-deformations is a new method in Riemann-Finsler geometry, it is introduced by the author(see arxiv:1209.0845). Later on I will…

In this paper, as an application of the inverse problem of calculus of variations, we investigate two compatibility conditions on the spherically symmetric Finsler metrics. By making use of these conditions, we focus our attention on the…

A relevant property of equifocal submanifolds is that their parallel sets are still immersed submanifolds, which makes them a natural generalization of the so-called isoparametric submanifolds. In this paper, we prove that the regular…

In this paper, we study a class of Finsler metrics which contains the class of P-reducible metrics. Finsler metrics in this class are called generalized P-reducible metrics. We consider generalized P-reducible metrics with scalar flag…

We consider metrics related to each other by functionals of a scalar field $\varphi(x)$ and it's gradient $\nabla \varphi(x)$, and give transformations of some key geometric quantities associated with such metrics. Our analysis provides…

In the Riemannian setting, every flat Cartan--Hadamard manifold is isometric to Euclidean space, the canonical model that underlies the theory of Sobolev spaces and guarantees the sharpness/rigidity of the Hardy inequality, the uncertainty…

The aim of this paper is to expose some geometrical properties of the locally Minkowski-Cartan space with the Berwald-Moor metric of momenta. This space is regarded as a particular case of the $m$-th root Cartan space. Thus, Section 2…

The Bochner tensor is the K\"ahler analogue of the conformal Weyl tensor. In this article, we derive local (i.e., in a neighbourhood of almost every point) normal forms for a (pseudo-)K\"ahler manifold with vanishing Bochner tensor. The…

In this paper we study isometry-invariant Finsler metrics on inner product spaces over $\mathbb{R}$ or $\mathbb{C}$, i.e. the Finsler metrics which do not change under the action of all isometries of the inner product space. We give a new…

In this paper, we study the integral curvatures of Finsler manifolds and prove several Myers type theorems.

In this paper, we consider the cylindrically symmetric Finsler metrics and we obtain their Douglas curvature. Furthermore, we obtain the differential equation system of the cylindrically symmetric Finsler metrics with vanishing Douglas…

This paper is a continuation of our investigation of the anisotropic conformal change of a conic pseudo-Finsler surface $(M,F)$, namely, the change $\overline{F}(x,y)=e^{\phi(x,y)}F(x,y)$ \cite{first paper}. We obtain the relationship…

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…

In this paper, we introduce a broad class of metrics on the slit tangent bundle of Finsler manifolds, termed \emph{$F$-natural metrics}. These metrics parallel the well-established $g$-natural metrics on the tangent bundles of Riemannian…

We determine the curvature equations of natural metrics on tangent bundles and radius r tangent sphere bundles S_rM of a Riemannian manifold M. A family of positive scalar curvature metrics on S_rM is found, for any M with bounded sectional…

In this paper, we study almost regular Landsberg general $(\alpha,\beta)$-metrics in Finsler geometry. The corresponding equivalent equations are given. By solving the equations, we give the classification of Landsberg general…

In this paper, we construct coordinates at the infinity of an asymptotically flat end of a Ricci-flat manifold $(M_m, g)$ as long as the $L^{m/2}$ norm of the curvature is finite in this end. As applications, we can define a Weyl tensor at…

We use two non-Riemannian curvature tensors, the $\chi$-curvature and the mean Berwald curvature to characterise a class of Finsler metrics admitting first integrals.

In this paper we describe an approach to complex Finsler metrics suitable to deal with global questions, and stressing the similarities between hermitian and complex Finsler metrics. Let $F$ be a smooth complex Finsler metric on a complex…