Related papers: Lectures on Finslerian Geometry
These notes concern linear transformations on R^n and C^n, exponentials of linear transformations, and some related geometric questions.
These informal notes deal with some basic properties of metric spaces, especially concerning lengths of curves.
Some general Finsler connections are defined. Emphasis is being made on the Cartan tensor and its derivatives. Vanishing of the hv-curvature tensors of these connections characterizes Landsbergian, Berwaldian as well as Riemannian…
These lectures are a brief introduction to supersymmetry.
We give a short introduction, beginning with the Kerr geometry itself, to the basic results, motivation, open problems and future directions of the Kerr/CFT correspondence.
The paper proposes a notion of volume element for Finsler spaces with metrics of Lorentzian signature, equipped with a time orientation. This notion is based on a slight modification of the idea of Holmes-Thompson volume element working for…
Notes to lectures on the epsilon calculus, covering axioms, semantics, completeness, and the first epsilon theorem.
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.…
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…
Rejoinder: Fisher Lecture: Dimension Reduction in Regression [arXiv:0708.3774]
We prove Hessian comparison theorems, Laplacian comparison theorems and volume comparison theorems of Finsler manifolds under various curvature conditions. As applications, we derive Mckean type theorems for the first eigenvalue of Finsler…
The present text is a collection of notes about differential geometry prepared to some extent as part of tutorials about topics and applications related to tensor calculus. They can be regarded as continuation to the previous notes on…
We describe the construction of the slice fibration of a given one.
The paper surveys open problems and questions related to geodesics defined by Riemannian, Finsler, semi Riemannian and magnetic structures on manifolds.
The generalized Finsler geometry, as well as Finsler geometry, is a generalization of Riemann geometry. The generalized Finsler geometry can be endowed with the Cartan connection. The generalized Finsler geometry and its Cartan connection…
We construct all Finsler metrics on the two-sphere for which geodesics are circles and show that any (reversible) path geometry on a two-dimensional manifold is locally the system of geodesics of a Finsler metric.
We lay foundations of the subject in the title, on which we build in another paper devoted to isometries in spaces of K\"ahler metrics.
We present our Finsler spacetime formalism which extends the standard formulation of Finsler geometry to be applicable in physics. Finsler spacetimes are viable non-metric geometric backgrounds for physics; they guarantee well defined…
The geometry on a slope of a mountain is the geometry of a Finsler metric, called here the {\it slope metric}. We study the existence of globally defined slope metrics on surfaces of revolution as well as the geodesic's behavior. A…
Some geometric structures with associated Riemannian metrics have been considered in the book.