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arXiv · 2303.06414

Finsler manifolds with Positive Weighted Flag Curvature

Zhongmin Shen·Runzhong Zhao
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Abstract

The flag curvature is a natural Finsler extension of the sectional curvature in Riemannian geometry. However, there are many non-Riemannian quantities which interact with the flag curvature. In this paper, we introduce a notion of weighted flag curvature by modifying the flag curvature using the non-Riemannian quantity, $T$-curvature. We show that a forward complete open Finsler manifold with positive weighted flag curvature is necessarily diffeomorphic to the Euclidean space, and that a compact Finsler manifold with nonnegative weighted flag curvature and strictly convex boundary is diffeomorphic to a Euclidean ball.

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Zhongmin Shen, Runzhong Zhao. 2023-03-11. Finsler manifolds with Positive Weighted Flag Curvature. https://arxiv.org/abs/2303.06414

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