** Riv.Mat.Univ.Parma (4) 17 (1991) **

**P. TAMIA DIMOPOULOU**

*On direction dependent f-structures satisfying* f^{s} + f^{t} = 0

**Pages:** 279-293

**Received:** 20 May 1991

**Mathematics Subject Classification:)** 53C60

**Abstract**
We consider tensor fields *f* ≠ 0 of type (1,1) satysfying *f*^{s} + *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* = 4*k* -1 and t =1, *sk* + 1 and t = 1. Also we define connections compatible with *f* (*s, **t*)-structures and we consider their properties.

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