Spray几何中的几何量及其在Finsler几何中的应用  

Geometric quantities in spray geometry and their applications in Finsler geometry

作　　者：李本伶 沈忠民 Benling Li;Zhongmin Shen

机构地区：[1]宁波大学数学与统计学院,宁波315211 [2]Department of Mathematical Sciences,Indiana University,Indianapolis,IN 46202,USA

出　　处：《中国科学：数学》2024年第10期1569-1584,共16页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:12071423);浙江省自然科学基金(批准号:LY23A010012);宁波市自然科学基金(批准号:2021J110)资助项目。

摘　　要：本文主要对spray几何研究进展作一个概要的综述和进一步理解.对spray几何中的S-曲率、χ-曲率和Ricci曲率等几何量进行探讨,重新给出它们之间的联系并探讨它们在局部射影平坦情形和射影等价情形的应用.介绍以上几何量在Finsler几何中的应用,主要包括Finsler度量的χ-曲率以及spray能否由Finsler度量诱导的逆问题的研究进展.In this paper,we mainly provide an overview and further comprehension of the progress of spray geometry.Some geometric quantities including S-curvature,χ-curvature,Ricci curvature,etc.in spray geometry are studied.We give a new proof of their relationship.Then their applications in the locally projectively flat case and the projectively equivalent case are discussed.We also introduce the applications of the above geometric quantities in Finsler geometry,mainly including the progress of the χ-curvature of Finsler metrics and the inverse problem of whether the spray can be induced by a Finsler metric.

关 键 词：FINSLER度量 SPRAY S-曲率 χ-曲率 RICCI曲率 

分 类 号：O186.1[理学—数学]