Hypersurfaces of semi-C-reducible and S4-like Finsler spaces

The notions of semi C-reducible and S4-like Finsler spaces have been introduced by Matsumoto and Shibata (6]). The object of the present paper is to study some properties of the hypersurfaces immersed in semi-C-reducible and S4-like Finsler spaces. It has been proved that a hypersurface of semi-C-reducible Finsler space is a semi-C-reducible while the condition, under with a hypersurface of S4-like Finsler space will be a S-4like space, has been obtained. The condition under which a hypersurface of semi-C-reducible Landsberg space will be a Landsberg space has also been obtained. After using the so called “T-condition” (Matsumoto 5]) we have discussed the condition under which a hypersurface of a semi-C-reducible Finsler spaceF _n satisfying T-condition will also satisfy T-condition.