Given a Riemannian manifold (M,

) with an almost Hermitian structure f and a non-vanishing covariant vector field b, consider the generalized Randers metric

, where

is a special singular Riemannian metric defined by b and f. This metric L is called an (a, b, f)-metric. We compute the inverse and the determinant of the fundamental tensor (

) of an (a, b, f)-metric. Then we determine the maximal domain D of

for an (a, b, f)-manifold where a y-local Finsler structure L is defined. And then we show that any (a, b, f)-manifold is quasi-C-reducible and find a condition under which an (a, b, f)-manifold is C-reducible.