Recently the present authors introduced a general class of Finsler connections which leads to a smart representation of connection theory in Finsler geometry and yields to a classification of Finsler connections into the three classes. Here the properties of one of these classes namely the Berwald-type connections which contains Berwald and Chern(Rund) connections as a special case is studied. ...

We show that the index of a lightlike geodesic in a conformally standard stationary spacetime (M0 × R, g) is equal to the index of its spatial projection as a geodesic of a Finsler metric F on M0 associated to (M0×R, g). Moreover we obtain the Morse relations of lightlike geodesics connecting a point p to a curve γ(s) = (q0, s) by using Morse theory on the Finsler manifold (M0, F ). To this end...

Some problems concerning to Liouville distribution and framed f -structures are studied on the normal bundle of the lifted Finsler foliation to its normal bundle. It is shown that the Liouville distribution of transversally Finsler foliations is an integrable one and some natural framed f(3, ε)structures of corank 2 exist on the normal bundle of the lifted Finsler foliation.

‎In this paper we study Finsler metrics with orthogonal invariance‎. ‎We‎ ‎find a partial differential equation equivalent to these metrics being locally projectively flat‎. ‎Some applications are given‎. ‎In particular‎, ‎we give an explicit construction of a new locally projectively flat Finsler metric of vanishing flag curvature which differs from the Finsler metric given by Berwald in 1929.

In this paper, we introduce and investigate a general transformation or change of Finsler metrics, which is referred to as a generalized β-conformal change: L(x, y) −→ L(x, y) = f(eL(x, y), β(x, y)). This transformation combines both β-change and conformal change in a general setting. The change, under this transformation, of the fundamental Finsler connections, together with their associated g...

In this paper we continue the study of the complex Beil metrics, in complex Finsler geometry, [18]. Primarily, we determine the main geometric objects corresponding to these metrics, e.g. the Chern-Finsler complex non-linear connection, the Chern-Finsler complex linear connection and the holomorphic curvature. We focus our study on the cases when a complex Finsler space, endowed with a complex ...

A Finsler space (M,Σ) is said to be geodesically reversible if each oriented geodesic can be reparametrized as a geodesic with the reverse orientation. A reversible Finsler space is geodesically reversible, but the converse need not be true. In this note, building on recent work of LeBrun and Mason [13], it is shown that a geodesically reversible Finsler metric of constant flag curvature on the...

This paper is devoted to a study of geodesics of Finsler metrics via Zermelo navigation. We give a geometric description of the geodesics of the Finsler metric produced from any Finsler metric and any homothetic field in terms of navigation representation, generalizing a result previously only known in the case of Randers metrics with constant S-curvature. As its application, we present explici...

After recalling the structure equations of Finsler structures on surfaces, I define a notion of ‘generalized Finsler structure’ as a way of micro-localizing the problem of describing Finsler structures subject to curvature conditions. I then recall the basic notions of path geometry on a surface and define a notion of ‘generalized path geometry’ analogous to that of ‘generalized Finsler structu...