On the special Finsler metric

Abstract

Given a Riemannian manifold (M,alpha ) with an almost Hermitianstructure f and a non-vanishing covariant vector field b,,consider the generalized Randers metric L=alpha +beta ,,where beta is a special singular Riemannian metric defined byb and f. This metric L is called an (a,b,f)-metric. Wecompute the inverse and the determinant of the fundamental tensor(g_{ij}) of an (a,b,f)-metric. Then we determine the maximaldomain mathcal{D}, of TMsetminus O, for an(a,b,f)-manifold where a y-local Finsler structure L, isdefined. And then we show that any (a,b,f)-manifold isquasi-C-reducible and find a condition under which an(a,b,f)-manifold is C-reducible.