Related papers: A general model for time-minimizing navigation on …
Finsler geometry naturally appears in the description of various physical systems. In this review I divide the emergence of Finsler geometry in physics into three categories: as dual description of dispersion relations, as most general…
We give an overview on the status and on the perspectives of Finsler gravity, beginning with a discussion of various motivations for considering a Finslerian modification of General Relativity. The subjects covered include Finslerian…
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…
Finslerian extension of the theory of relativity implies that space-time can be not only in an amorphous state which is described by Riemann geometry but also in ordered, i.e. crystalline states which are described by Finsler geometry.…
We consider the Zermelo navigation problem on the ellipsoid of revolution (spheroid) in the presence of a perturbation $W$ determined by a mild velocity vector field, $|W|<1$, with application of Finsler metric of Randers type in the…
In this work, we extend for the first time the spherically symmetric Schwarzschild and Schwarzschild-De Sitter solutions with a Finsler-Randers-type perturbation which is generated by a covector $A_\gamma$. This gives a locally anisotropic…
Finslerian extensions of Special and General Relativity -- commonly referred to as Very Special and Very General Relativity -- necessitate the development of a unified Lorentz-Finsler geometry. However, the scope of this geometric framework…
For every Finsler metric $F$ we associate a Riemannian metric $g_F$ (called the Binet-Legendre metric). The transformation $F \mapsto g_F$ is $C^0$-stable and has good smoothness properties, in contrast to previous constructions. The…
Finsler geometry is a natural and fundamental generalization of Riemann geometry. The Finsler structure depends on both coordinates and velocities. It is defined as a function on tangent bundle of a manifold. We use the Bianchi identities…
Finsler geometry is a natural and fundamental generalization of Riemann geometry, and is a tool to research Lorentz invariance violation. We find the connection between the most general modified dispersion relation and a pseudo-Finsler…
The proposal of this work is to provide an answer to the following question: is it possible to treat the metric of space-time - that in General Relativity (GR) describes the gravitational interaction - as an effective geometry? In other…
Finsler geometry is a natural generalization of pseudo-Riemannian geometry. It can be motivated e.g. by a modified version of the Ehlers-Pirani-Schild axiomatic approach to space-time theory. Also, some scenarios of quantum gravity suggest…
This PhD dissertation covers a range of topics in Finsler geometry and Finsler gravity, most notably: (i) the characterization of Berwald spaces, (ii) pseudo-Riemann (non-)metrizability of Berwald spaces, (iii) $(\alpha,\beta)$-metrics,…
We develop the kinematics in Matrix Gravity, which is a modified theory of gravity obtained by a non-commutative deformation of General Relativity. In this model the usual interpretation of gravity as Riemannian geometry is replaced by a…
We construct gravitational dynamics for Finsler spacetimes in terms of an action integral on the unit tangent bundle. These spacetimes are generalizations of Lorentzian metric manifolds which satisfy necessary causality properties. A…
The techniques and analysis presented in this thesis provide new methods to solve optimization problems posed on Riemannian manifolds. These methods are applied to the subspace tracking problem found in adaptive signal processing and…
We review recent developments in cosmological models based on Finsler geometry and extensions of general relativity within this framework. Finsler geometry generalizes Riemannian geometry by allowing the metric tensor to depend on position…
Geometric mechanics models of locomotion have provided insight into how robots and animals use environmental interactions to convert internal shape changes into displacement through the world, encoding this relationship in a ``motility…
We present a generalization of the spinor and twistor geometry for on (pseudo) Riemannian manifolds enabled with nonholonomic distributions or for Finsler-Cartan spaces modelled on tangent Lorentz bundles. Nonholonomic (Finsler) twistors…
In this paper we study the sub-Finsler geometry as a time-optimal control problem. In particular, we consider non-smooth and non-strictly convex sub-Finsler structures associated with the Heisenberg, Grushin, and Martinet distributions.…