P. TAMIA DIMOPOULOU
On direction dependent f-structures satisfying fs + ft = 0
Received: 20 May 1991
Mathematics Subject Classification:) 53C60
Abstract We consider tensor fields f ≠ 0 of type (1,1) satysfying fs + f t = 0 depending on both point and direction on a manifold. These fields define the direction-dependent f (s, t)-structures. Starting with a Finsler f (s, t)-structure on a manifold N we introduce an horizontal f (s, t)-structure on N and an f(s, t)-structure on TN. Next we prove two necessary and sufficient conditions for a manifold to admit a Finsler f(s, t)-structure in cases = t + 2, s = 4k -1 and t =1, sk + 1 and t = 1. Also we define connections compatible with f (s, t)-structures and we consider their properties.