一类具有弱射影Ricci曲率的Spray及其可度量化问题  

On a Class of Spray of Weakly Projective Ricci Curvature and Its Finsler Metrizability

作　　者：程新跃 龚妍廿 李明 CHENG Xinyue;GONG Yannian;LI ming(School of Mathem atical Sciences,Chongqing Normal University,Chongqing 401331;School of Sciences,Chongqing University of Technology,Chongqing 400054,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331 [2]重庆理工大学理学院,重庆400054

出　　处：《重庆师范大学学报（自然科学版）》2019年第6期58-63,共6页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金（No.11871126;No.11571184）;重庆师范大学科学研究基金（No.17XLB022）

摘　　要：【目的】Spray的曲率性质及其可度量化问题在Spray几何中是很重要的,因此对一类由Funk度量Θ构造的射影平坦的Spray G(其测地系数为G^i=τΘy^i,其中τ是常数)进行研究。【方法】计算G的射影Ricci曲率,进而在一定射影Ricci曲率条件下研究这类Spray的可度量化问题。【结果】1)在G是射影Ricci-平坦的条件下,确定了流形的体积形式;2)在G可由芬斯勒度量F诱导的前提下,若F具有弱射影Ricci曲率且是非射影Ricci-平坦的,则F~的结构可被确定。【结论】初步分类了具有弱射影Ricci曲率的芬斯勒度量F。[Purposes]It is important to study the curvature properties and Finsler metrizability of a Spray in Spray geometry.It makes sense to study a kind of projective flat Spray G constructed by Funk metricΘ,which satisfying G^i=τΘy^i and τ is a constant.[Methods]Calculating the projective Ricci curvature of G .Furthermore,the Finsler metrizability of G can be studied under certain conditions of projective Ricci curvature.[Findings]On the one hand,under the condition that G is projective Ricci flat,the volume form of manifold can be determined.On the other hand,suppose G can be induced by Finsler metric F with weak projective Ricci curvature and not projective Ricci flat,then the structure of F can be determined.[Conclusions]The Finsler metric F with weak projective Ricci curvature is preliminarily classified here.

关 键 词：射影Ricci曲率 Funk度量 SPRAY Spray可度量化 

分 类 号：O186.15[理学—数学]