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LetF n be a Finsler space with metric functionF(x, y). M. Matsumoto [6] has defined a modified Finsler spaceF

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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.

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In this paper, we study a class of Finsler metrics defined by a Riemannian metric and a 1-form on a manifold. We find an equation that characterizes Douglas metrics on a manifold of dimension n ≧ 3.

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