On the projective Ricci curvature In Memory of Professor Zhengguo Bai(1916-2015)

来源 :中国科学：数学（英文版） | 被引量 : 0次 | 上传用户：yuhui269

【摘要】

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【作者】

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Zhongmin Shen Liling Sun

【机构】

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Department of Mathematical Sciences,Indiana University-Purdue University Indianapolis,Indianapolis,I

【出处】

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中国科学：数学（英文版）

【发表日期】

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2021年7期

【关键词】

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spray Finsler metric Randers metric projective Ricci curvature

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The notion of the Ricci curvature is defined for sprays on a manifold.With a volume form on a manifold,every spray can be deformed to a projective spray.The Ricci curvature of a projective spray is called the projective Ricci curvature.In this paper,we introduce the notion of projectively Ricci-flat sprays.We establish a global rigidity result for projectively Ricci-flat sprays with nonnegative Ricci curvature.Then we study and characterize projectively Ricci-flat Randers metrics.

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On the projective Ricci curvature In Memory of Professor Zhengguo Bai(1916-2015)

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