Properties of Generalized Berwald Connections

Properties of Generalized Berwald Connections

Generalized Symmetric Berwald Spaces

In this paper we study generalized symmetric Berwald spaces. We show that if a Berwald space $(M,F)$ admits a parallel $s-$structure then it is locally symmetric. For a complete Berwald space which admits a parallel s-structure we show that if the flag curvature of $(M,F)$ is everywhere nonzero, then $F$ is Riemannian.

On BC-generalized Landsberg Finsler metrics

Equality of hh -curvatures of the Berwald and Cartan connections leads to a new class of Finsler metrics, socalled BC-generalized Landsberg metrics. Here, we prove that every BC-generalized Landsberg metric of scalar flag curvature with dimension greater than two is of constant flag curvature.

The Berwald-type connection associated to time-dependent second-order differential equations

We investigate the notions of a connection of Finsler type and of Berwald type on the first jet bundle J1π of a manifold E which is fibred over IR. Such connections are associated to a given horizontal distribution on the bundle π0 1 : J 1π → E, which in particular may come from a time-dependent system of second-order ordinary differential equations. In order to accomodate three existing constr...

Generalization of Hashiguchi–Ichijyō’s Theorems to Wagner–type manifolds

We introduced a class of conformally invariant Ehresmann connections so–called L-horizontal endomorphism in [7]. Using this class, we define conformally invariant manifolds: Wagner–type manifold and locally Minkowski–type manifold as special generalized Berwald manifolds. Then a generalization of Hashiguchi–Ichijyō’s Theorems to Wagner–type manifolds is presented. Mathematics Subject Classifica...