Amirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24492220210901Some fundamental problems in global Finsler geometry185198445610.22060/ajmc.2021.20219.1060ENXinyueChengSchool of Mathematical Sciences
Chongqing Normal University
Chongqing, China0000-0003-2522-9189Journal Article20210630The geometry and analysis on Finsler manifolds is a very important part of Finsler geometry. In this survey 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. Further, we also obtain an estimate of lower bound for the non-zero eigenvalues of the Finsler Laplacian under the condition that $\mathrm{Ric}_{N}\geq K >0 $.https://ajmc.aut.ac.ir/article_4456_e00e8a7fc9707694ccf2ae6105c2af0e.pdf