• 대한수학회보
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• 제37권3호
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• pp.543-550
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• 2000

We prove that every generalized Landsberg manifold of scalar curvature R is a Riemannian manifold of constant curvature, provided that $R\neq\ 0$.

• 대한수학회논문집
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• 제39권1호
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• pp.187-199
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• 2024

In the present paper, following the pullback approach to Finsler geometry, we study intrinsically the C^v-reducible and generalized C^v-reducible Finsler spaces. Precisely, we introduce a coordinate-free formulation of these manifolds. Then, we prove that a Finsler manifold is C^v-reducible if and only if it is C-reducible and satisfies the 𝕋-condition. We study the generalized C^v-reducible Finsler manifold with a scalar π-form 𝔸. We show that a Finsler manifold (M, L) is generalized C^v-reducible with 𝔸 if and only if it is C-reducible and 𝕋 = 𝔸. Moreover, we prove that a Landsberg generalized C^v-reducible Finsler manifold with a scalar π-form 𝔸 is Berwaldian. Finally, we consider a special C^v-reducible Finsler manifold and conclude that a Finsler manifold is a special C^v-reducible if and only if it is special semi-C-reducible with vanishing 𝕋-tensor.