Linear transformations of Finsler connections

Finsler Connections in Generalized Lagrange Spaces

The Chern–Rund connection from Finsler geometry is settled in the generalized Lagrange spaces. For the geometry of these spaces, we refer to [5]. Mathematics Subject Classification: 53C60

Transformations of Sheaf Connections

After a brief survey of the primary ideas involved in the theory of connections on vector and principal sheaves (studied in [7], [8], [14], [15]), we examine the behaviour of connections under various types of morphisms between sheaves of the considered category. The results thus obtained are useful in the development of a non-smooth geometry in the aforementioned abstract framework and related...

A classification of some Finsler connections and their applications

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 structures. This view point makes it possible to give a smart representation of connection theory in Finsler geometry and yields to a classification of Finsler connec...

On One-Sided Ideals of Rings of Linear Transformations

Geometric Objects Associated with the Fundamental Connections in Finsler Geometry

The aim of the present paper is to provide an intrinsic investigation of the fundamental properties of the most important geometric objects associated with the fundamental linear connections on a Finsler manifold. We introduce and investigate intrinsically the most general properties concerning the torsion tensor fields and the curvature tensor fields associated with a certain regular connectio...