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Einstein Finsler metrics and Killing vector fields on Riemannian manifolds 被引量:2
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作者 CHENG XinYue SHEN ZhongMin 《Science China Mathematics》 SCIE CSCD 2017年第1期83-98,共16页
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 o... 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 S^3 with Ric = 2F^2, Ric = 0 and Ric =-2F^2, 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. 展开更多
关键词 Killing vector field Finsler metric (α β)-metric Ricci curvature Einstein metric Ricci-flat metric
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De Lellis-Topping type inequalities on smooth metric measure spaces
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作者 Meng MENG Shijin ZHANG 《Frontiers of Mathematics in China》 SCIE CSCD 2018年第1期147-160,共14页
We obtain some De Lellis-Topping type inequalities on the smootla metric measure spaces, some of them are as generalization of De Lellis-Topping type inequality that was proved by X. Cheng [Ann. Global Anal. Geom., 20... We obtain some De Lellis-Topping type inequalities on the smootla metric measure spaces, some of them are as generalization of De Lellis-Topping type inequality that was proved by X. Cheng [Ann. Global Anal. Geom., 2013, 43: 153-160]. 展开更多
关键词 De Lellis-Topping type inequality Bakry-Emery Ricci curvature smooth metric measure space
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Gap results for compact quasi-Einstein metrics
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作者 Linfeng Wang 《Science China Mathematics》 SCIE CSCD 2018年第5期943-954,共12页
In this paper, we work on compact quasi-Einstein metrics and prove several gap results. In the first part, we get a gap estimate for the first nonzero eigenvalue of the weighted Laplacian, by establishing a comparison... In this paper, we work on compact quasi-Einstein metrics and prove several gap results. In the first part, we get a gap estimate for the first nonzero eigenvalue of the weighted Laplacian, by establishing a comparison theorem for the weighted heat kernel. In the second part, we establish two gap results for the Ricci curvature and the scalar curvature, based on which some rigid properties can be derived. 展开更多
关键词 quasi-Einstein metric heat kernel eigenvalue diameter Ricci curvature scalar curvature gap result
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