Related papers: Finsleroid--Finsler Parallelism

The paper contributes to the important and urgent problem to extend the physical theory of space-time in a Finsler-type way under the assumption that the isotropy of space is violated by a single geometrically distinguished spatial…

The method of simple straightforward calculation of the curvature tensor of the Finsleroid--regular space is indicated. The Schwarzschild metric which underlines the gravitational field produced by static spherical-symmetric body is shown…

We show that always present in the autoparallels, even in natural liftings to the Finsler bundle of arbitrary connections, the Lorentz force is inescapable in Finsler geometry. These liftings retain the form $R_{\,\nu \lambda }^{\mu }\omega…

This paper presents a new type of surface models constructed on the basis of Finsler geometry. A Finsler metric is defined on the surface by using an underlying vector field, which is an in-plane tilt order. According to the orientation of…

We show that in dimension 2 every Finsler metric with at least 3-dimensional Lie algebra of projective vector fields is locally projectively equivalent to a Randers metric. We give a short list of such Finsler metrics which is complete up…

We briefly review some basic concepts of parallel displacement in Finsler geometry. In general relativity, the parallel translation of objects along the congruence of the fundamental observer corresponds to the evolution in time. By…

In this note we make use of some properties of vector fields on a manifold to give an alternate proof to [3] for the equivalence between connections and parallel transport on vector bundles over manifolds. Out of the proof will emerge a new…

We found a necessary and sufficient condition for the existence of the tensor product of modules over a vertex algebra. We defined the notion of vertex bilinear map and we provide two algebraic construction of the tensor product, where one…

Horizontal endomorphisms, almost complex structures, vertical, horizontal and complete lifts on prolongation of a Lie algebroid are considered. Then using exact sequences, semisprays are constructed. Moreover, important geometrical objects…

A linear connection on a Finsler manifold is called compatible to the Finsler function if its parallel transports preserve the Finslerian length of tangent vectors. Generalized Berwald manifolds are Finsler manifolds equipped with a…

Let (M1,F1) and (M2,F2) be two Finsler manifolds. The twisted product Finsler metric of F1 and F2 is a Finsler metric F = (F1^2+ f^2F2^2)^1/2 endowed on the product manifold M1 * M2, where f is a positive smooth function on M1 * M2. In this…

We investigate a Maclaurin inequality for vectors and its connection to an Aleksandrov-type inequality for parallelepipeds.

We show that which that for a Berwald structure, any Riemannian structure that is preserved by the Berwald connection leaves the indicatrix invariant under horizontal parallel transport. We also obtain the converse result: if $({\bf M},F)$…

We show that, under suitable hypotheses, the foundation of a generalized parallel connection of matroids is the relative tensor product of the foundations. Using this result, we show that the foundation of a 2-sum of matroids is the…

Generalized Berwald manifolds are Finsler manifolds admitting linear connections such that the parallel transports preserve the Finslerian length of tangent vectors (compatibi\-li\-ty condition). By the fundamental result of the theory…

In this paper, we consider Randers change of some special $ (\alpha, \beta)- $ metrics. First we find the fundamental metric tensor and Cartan tensor of these Randers changed $ (\alpha, \beta)- $metrics. Next, we establish a general formula…

Paravectors just like integers have a ring structure. By introducing an integrated product we get geometric properties which make paravectors similar to vectors. The concepts of parallelism, perpendicularity and the angle are conceptually…

A linear connection on a Finsler manifold is called compatible to the metric if its parallel transports preserve the Finslerian length of tangent vectors. Generalized Berwald manifolds are Finsler manifolds equipped with a compatible linear…

Generalized Berwald manifolds are Finsler manifolds admitting linear connections such that the parallel transports preserve the Finslerian length of tangent vectors. By the fundamental result of the theory \cite{V5} such a linear connection…

We establish a tensor product theorem for slope semistable parabolic $\lambda$-connections over smooth projective varieties in arbitrary characteristic.