On a U-birecurrent finsler space

الملخص EN

The normal projective Finsler connection coefficients have been by defined K.Yano [6].

The components of the curvature tensor with respect to normal projective connection coefficients have also been discussed .

H.D.Pande and S.K.Tiwari [2] introduced the second order recurrence of the curvature tensor ( hv - curvature tensor ) in Finsler space with respect to Cartan's connection .

F.Y.A.

Qasem [4] discussed the recurrence of the curvature tensor in Finsler space with respect to Berwald's connection and he denoted such space by UR - Finsler space.

The purpose of the present paper is to introduce the birecurrence of the curvature tensor in Finsler space with respect to Berwald's connection .

Such space in which the curvature tensor is birecurrent is denoted by UBR – Fn .

Different results have been obtained in this space and certain properties of such space have been searched out .

We discuss the recurrence curvature tensor field of second order and we deal with its properties of an UBR – Fn .

Finally , we discuss the relation of this space with a space in which Douglas curvature tensor is birecurrent and we obtain the necessary condition for Finsler space to be UBR – Fn when Douglas curvature tensor and Ricci tensor are birecurrent .

Key words : Birecurrent Finsler Space, Second Order Recurrent , Douglas Birecurrent Tensor .