A new approach to generalized Berwald manifolds

Abstract. A large class of special Finsler manifolds can be endowed with Finsler connections whose “h-part ” does not depend on the directions. We call these Finsler connections h-basic and present a systematic treatment of them, using (in a simplified form) the Frölicher-Nijenhuis calculus. We provide an axiomatic description of a distinguished class of h-basic Finsler connections, the class of Ichijyo ̄ connections. With the help of an Ichijyo ̄ connection we present new characterizations of generalized Berwald manifolds, as well as – in particular – of Berwald manifolds and locally Minkowski manifolds