Bull. Korean Math. Soc. 2003 Vol. 40, No. 3, 457-464 Published online September 1, 2003

Nany Lee The University of Seoul

Abstract : Given a Riemannian manifold $(M,\alpha )$ with an almost Hermitian structure $f$ 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 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 $(g_{ij})$ of an $(a,b,f)$-metric. Then we determine the maximal domain $\mathcal{D}\,$ of $TM\setminus O\,$ 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.