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Demonstrates a new curvature formula and explores the Landsberg property in Finsler geometry, indicating important implications for geometric properties.
In this paper, we provide a new Riemann curvature formula in homogeneous Finsler geometry. Meanwhile, we prove that a homogeneous Finsler metric is Landsberg if and only if its connection operator induces Killing vector fields for a Hessian metric. As an application, we prove that any homogeneous Landsberg sphere with dimension bigger than 1 and constant flag curvature must be Riemannian.
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Xu et al. (2026) studied this question.
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