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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