Navigation Finsler metrics on a gradient Ricci soliton  

作　　者：LI Ying MO Xiao-huan WANG Xiao-yang 

机构地区：[1]Department of Applied Mathematics,Zhejiang University of Technology,Hangzhou 310023,China [2]Key Laboratory of Pure and Applied Mathematics,School of Mathematical Sciences,Peking University,Beijing 100871,China [3]School of Mathematics and Statistics,Beijing Institute of Technology,Beijing 100081,China

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2024年第2期266-275,共10页高校应用数学学报（英文版）（B辑）

基　　金：Supported by the National Natural Science Foundation of China(11771020,12171005).

摘　　要：In this paper,we study a class of Finsler metrics defined by a vector field on a gradient Ricci soliton.We obtain a necessary and sufficient condition for these Finsler metrics on a compact gradient Ricci soliton to be of isotropic S-curvature by establishing a new integral inequality.Then we determine the Ricci curvature of navigation Finsler metrics of isotropic S-curvature on a gradient Ricci soliton generalizing result only known in the case when such soliton is of Einstein type.As its application,we obtain the Ricci curvature of all navigation Finsler metrics of isotropic S-curvature on Gaussian shrinking soliton.

关 键 词：gradient Ricci soliton navigation Finsler metric isotropic S-curvature Ricci curvature Gaussian shrinking soliton 

分 类 号：O186.1[理学—数学]