A Study of P*-Reducible Finsler Space with Douglas Tensor

Abstract

In this paper we consider a Finsler space whose v (hv)-
torsion tensor
ijk P is given by
( ) ijk P = λCijk + μ hijCk + hjkCi + hkiCj
where μ & λ are scalar functions positively homogeneous of
degree one in yi and call such a Finsler space as P∗ − reducible
Finsler space. We have also proved that a P∗ − Randers space
with vanishing Douglas tensor is a Riemannian space if the
dimension is greater than three. Also we have worked out the role
of P∗ − reducibility condition in special Finsler spaces.