Some fundamental problems in global Finsler geometry

2019/10/18 by Xinyue Cheng, Cheng, Xinyue · 1 citation
Physics and Astronomy · #Advanced Differential Geometry Research #Cosmology and Gravitation Theories #Differential Geometry (math.DG) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1910.08267

openalex publication_date 2019/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The geometry and analysis on Finsler manifolds is a very important part of Finsler geometry. In this article, we introduce some important and fundamental topics in global Finsler geometry and discuss the related properties and the relationships in them. In particular, we optimize and improve the various definitions of Lie derivatives on Finsler manifolds. We also characterize the gradient vector fields and obtain a gradient estimate for any smooth function on a Randers manifold.

Citations

• Comparison theorems in Finsler geometry and their applications

Cited by

• Some important applications of improved Bochner inequality on Finsler manifolds

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