关于射影Ricci曲率的比较定理与共形不变性

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英文篇名：On the Comparison Theorem and Conformal Invariance of a Projective Ricci Curvature 作者：程新跃 ; 李婷婷 ; 殷丽 英文作者：CHENG Xin-yue;LI Ting-ting;YIN Li;School of Mathematical Sciences,Chongqing Normal University;You Can Secondary School Department,Chongqing New Oriental Training School; 关键词：芬斯勒度量 ; 射影Ricci曲率 ; Ricci曲率 ; S-曲率 ; 共形相关 英文关键词：Finsler metric;;projective Ricci curvature;;Ricci curvature;;S-curvature;;conformally related 中文刊名：XNND 英文刊名：Journal of Southwest University(Natural Science Edition) 机构：重庆师范大学数学科学学院;重庆新东方培训学校优能中学部; 出版日期：2019-01-25 出版单位：西南大学学报(自然科学版) 年：2019 期：v.41;No.290 基金：国家自然科学基金项目(11871126);; 重庆师范大学科学研究基金项目(17XLB022) 语种：中文; 页：XNND201902009 页数：8 CN：02 ISSN：50-1189/N 分类号：58-65

摘要

主要研究了芬斯勒度量的射影Ricci曲率.首先,在一个完备的芬斯勒流形上,证明了关于芬斯勒度量的射影Ricci曲率的一个比较定理.其次,刻画了两个共形相关的芬斯勒度量的射影Ricci曲率的关系.在此基础上,证明了两个位似相关的芬斯勒度量的射影Ricci曲率是相等的.
        In this paper,we study the projective Ricci curvature in Finsler geometry.First,we obtain that a comparison theorem on the projective Ricci curvature on a complete Finsler manifold.Then,we characterize the relations between two projective Ricci curvatures for two conformally related Finsler metrics on a manifold.On this basis,we prove that if two Finsler metrics are homothetically related,then their projective Ricci curvatures are equal.

引文

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