TY - JOUR
ID - 4456
TI - Some fundamental problems in global Finsler geometry
JO - AUT Journal of Mathematics and Computing
JA - AJMC
LA - en
SN - 2783-2449
AU - Cheng, Xinyue
AD - School of Mathematical Sciences
Chongqing Normal University
Chongqing, China
Y1 - 2021
PY - 2021
VL - 2
IS - 2
SP - 185
EP - 198
KW - Dual Finsler metric
KW - Gradient vector field
KW - Finsler Laplacian
KW - eigenvalue
KW - Hessian
KW - Lie derivative
KW - weighted Ricci curvature
DO - 10.22060/ajmc.2021.20219.1060
N2 - The 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 $.
UR - https://ajmc.aut.ac.ir/article_4456.html
L1 - https://ajmc.aut.ac.ir/article_4456_e00e8a7fc9707694ccf2ae6105c2af0e.pdf
ER -