• Communications of the Korean Mathematical Society
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• v.39 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.40 no.3
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• pp.457-464
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• 2003

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 D of $TM{\backslash}O$ 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.

• Bulletin of the Korean Mathematical Society
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• v.37 no.3
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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 $R\neq\ 0$.

• Journal of the Korean Mathematical Society
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• v.61 no.1
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• pp.149-160
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• 2024

In this paper, we study the unicorn's Landsberg problem from an intrinsic point of view. Precisely, we investigate a coordinate-free proof of Numata's theorem on Landsberg spaces of scalar curvature. In other words, following the pullback approach to Finsler geometry, we prove that all Landsberg spaces of dimension n ≥ 3 of non-zero scalar curvature are Riemannian spaces of constant curvature.