On a class of projectively Ricci-flat Finsler metrics |
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| Affiliation: | 1. College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, PR China;2. Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, School of Mathematics and Information Science, Henan Normal University, 453007, PR China |
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| Abstract: | Every Finsler metric induces a spray 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. The projective Ricci curvature is an important projective invariant in Finsler geometry. In this paper, we study and characterize projectively Ricci-flat square metrics. Moreover, we construct some nontrivial examples on such Finsler metrics. |
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| Keywords: | Finsler metric Square metric Projective Ricci curvature Projectively Ricci-flat |
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