Special Types of Generalized

Alaa A. Abdallah1, A.A. Navlekar2 and Kirtiwant P. Ghadle1

1Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, 431004, INDIA.
2Department of Mathematics, Pratishitan Mahavidyalaya, Paithan (M.S.) INDIA.


In this paper, we introduced a Finsler space which Cartan's second curvature tensor Pjkhi satisfies a generalized recurrence property the sense of Berwald, i.e. characterized by the following condition

Bl Pjkhi = λi Pjkhi + μi ( δji gkh – δki gjh ) , Pjkhi ≠ 0 ,

where Bi is Berwald’s covariant differential operator with respect to xl , λi and μi are known as recurrence vectors, such space is called a generalized BP-recurrent space.

The purpose of the present paper to prove the above space can’t be an affinely connected space and we proved the above space can’t be a Landsberg space. Also we used properties of P2-Like space in above space and we got a new space it called P2-Like generalized BP-recurrent space. Also we obtained different theorems for some tensors which satisfy in above space.

Keywords :a generalized ?P?recurrent space, an affinely connected space, a Landsberg space, P2-Like space.

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