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.
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)
出处
《重庆师范大学学报（自然科学版）》
CAS
北大核心
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）
