芬斯勒—里奇流下若干几何量的演化  

On Evolutions of Some Geometric Quantities Under Finsler-Ricci Flow

作　　者：程新跃 吴朋生 CHENG Xinyue;WU Pengsheng(School of Mathematical Sciences,Chongqing Normal University,Chongqing,401331,P.R.China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《数学进展》2024年第3期529-541,共13页Advances in Mathematics（China）

基　　金：国家自然科学基金(Nos.12371051,12141101,11871126)。

摘　　要：本文主要研究了芬斯勒几何中若干重要的几何量沿芬斯勒—里奇流的变化规律.我们首先在芬斯勒—里奇流下得到了若干基本几何量的演化方程,它们对关于芬斯勒—里奇流的研究是至关重要的.进一步,我们在芬斯勒—里奇流下刻画了芬斯勒度量的测地系数和S-曲率的演化规律.This paper mainly studies the evolution equations of some important geometric quantities in Finsler geometry along Finsler-Ricci flow.First,we obtain the evolution equations of some fundamental geometric quantities under Finsler-Ricci flow,which are extreme important for the studies of Finsler-Ricci flow.Further,we characterize the evolution laws of geodesic coefficients and S-curvature of Finsler metrics under Finsler-Ricci flow.

关 键 词：芬斯勒—里奇流 RICCI曲率 Cartan张量 测地系数 S-曲率 

分 类 号：O186.14[理学—数学]