A classification of some Finsler connections and their applications

Abstract

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 viewpoint makes it possible to give a smart representation of connection theory in Finsler geometry and yields a classification of Finsler connections. Some practical applications of these connections are also considered.