Einstein Finsler metrics and killing vector fields on Riemannian manifolds

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• 作者：XinYue Cheng ; ZhongMin Shen
• 关键词：Killing vector field ; Finsler metric ; (a ; ß) ; metric ; Ricci curvature ; Einstein metric ; Ricci ; flat metric
• 刊名：Science China Mathematics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：60
• 期：1
• 页码：83-98
• 全文大小：234KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Applications of Mathematics;
• 出版者：Science China Press
• ISSN：1869-1862
• 卷排序：60

文摘

We use a Killing form on a Riemannian manifold to construct a class of Finsler metrics. We find equations that characterize Einstein metrics among this class. In particular, we construct a family of Einstein metrics on S3 with Ric = 2F2, Ric = 0 and Ric = -2F2, respectively. This family of metrics provides an important class of Finsler metrics in dimension three, whose Ricci curvature is a constant, but the flag curvature is not.