On compatible linear connections with totally anti-symmetric torsion tensor of three-dimensional generalized Berwald manifolds

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.

Spin(9)-structures and Connections with Totally Skew-symmetric Torsion

We study Spin(9)-structures on 16-dimensional Riemannian manifolds and characterize the geometric types admitting a connection with totally skew-symmetric torsion.

Properties of Generalized Berwald Connections

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. ...

properties of generalized berwald connections