The flag curvature is a natural extension of the sectional curvature in Riemannian geometry, and the S-curvature is a non-Riemannian quantity which vanishes for Riemannian metrics. There are (incomplete) nonRiemannian Finsler metrics on an open subset in Rn with negative flag curvature and constant S-curvature. In this paper, we are going to show a global rigidity theorem that every Finsler met...

It is shown that, on a manifold with a Finsler metric of Lorentzian signature, the lightlike geodesics satisfy the following variational principle. Among all lightlike curves from a point q (emission event) to a timelike curve γ (worldline of receiver), the lightlike geodesics make the arrival time stationary. Here “arrival time” refers to a parametrization of the timelike curve γ. This variati...

We study Finsler black holes induced from Einstein gravity as possible effects of quantum spacetime noncommutativity. Such Finsler models are defined by nonholonomic frames not on tangent bundles but on (pseudo) Riemannian manifolds being compatible with standard theories of physics. We focus on noncommutative deformations of Schwarzschild metrics into locally anisotropic stationary ones with s...

We locally classify all SO(3)-invariant four-dimensional pseudo-Finsler Berwald structures. These are Finslerian geometries which closest to (spatially, or SO(3))-spherically symmetric pseudo-Riemannian ones — and serve as ansatz find solutions of Finsler gravity equations generalize the Einstein equations. that there exist five classes non-pseudo-Riemannian (i.e. non-quadratic in velocities) S...

In this paper, we introduce a new deformable model for image segmentation, by reformulating a region based active contours energy into a geodesic contour energy involving a Finsler metric. As a result, we solve the region based active contours energy minimization problem without resorting to level set functions, but using a robust Eikonal equation framework. By sampling a set of control points ...

We synthesize and extend the previous ideas about appearance of both noncommutative and Finsler geometry in string theory with nonvanishing B–field and/or anholonomic (super) frame structures [42, 43, 48, 50]. There are investigated the limits to the Einstein gravity and string generalizations containing locally anisotropic structures modeled by moving frames. The relation of anholonomic frames...

This paper is connected with the problem of describing path metric spaces which are homeomorphic to manifolds and biLipschitz homogeneous, i.e., whose biLipschitz homeomorphism group acts transitively. Our main result is the following. LetX = G/H be a homogeneous space of a Lie group G, and let d be a geodesic distance on X inducing the same topology. Suppose there exists a subgroup GS of G whi...

In this paper we describe the Einstein-Kähler metric for the Cartan-Hartogs domains which are the special case of the Hua domains. First of all, we reduce the Monge-Ampère equation for the metric to an ordinary differential equation in the auxiliary function X = X(z, w). This differential equation can be solved to give an implicit function in X. Secondly, for some cases, we obtained explicit fo...

In this paper we prove several multiplicity results of t-periodic light rays in conformally stationary spacetimes using the Fermat metric and the extensions of the classical theorems of Gromoll-Meyer and Bangert-Hingston to Finsler manifolds. Moreover, we exhibit some stationary spacetimes with a finite number of t-periodic light rays and compute a lower bound for the period of the light rays w...

Abstract Finsler geometry is a natural arena to investigate the physics of spacetimes with local Lorentz violation. The directional dependence metric provides way encode Lorentz-violating effects into geometric structure spacetime. Here, classical field theory proposed in special geometry, so-called Randers-Finsler spacetime, where violation produced by background vector field. By promoting dif...