We show that on a Sasakian 3-sphere the Sasaki-Ricci flow initiating from a Sasakian metric of positive transverse scalar curvature converges to a gradient Sasaki-Ricci soliton.We also show the existence and uniquenes...We show that on a Sasakian 3-sphere the Sasaki-Ricci flow initiating from a Sasakian metric of positive transverse scalar curvature converges to a gradient Sasaki-Ricci soliton.We also show the existence and uniqueness of gradient Sasaki-Ricci soliton on each Sasakian 3-sphere.展开更多
This paper is the sequel to our study of heat kernel on Ricci shrinkers[29].In this paper,we improve many estimates in[29]and extend the recent progress of Bamler[2].In particular,we drop the compactness and curvature...This paper is the sequel to our study of heat kernel on Ricci shrinkers[29].In this paper,we improve many estimates in[29]and extend the recent progress of Bamler[2].In particular,we drop the compactness and curvature boundedness assumptions and show that the theory of F-convergence holds naturally on any Ricci flows induced by Ricci shrinkers.展开更多
In this paper,we study a class of Finsler metrics defined by a vector field on a gradient Ricci soliton.We obtain a necessary and sufficient condition for these Finsler metrics on a compact gradient Ricci soliton to b...In this paper,we study a class of Finsler metrics defined by a vector field on a gradient Ricci soliton.We obtain a necessary and sufficient condition for these Finsler metrics on a compact gradient Ricci soliton to be of isotropic S-curvature by establishing a new integral inequality.Then we determine the Ricci curvature of navigation Finsler metrics of isotropic S-curvature on a gradient Ricci soliton generalizing result only known in the case when such soliton is of Einstein type.As its application,we obtain the Ricci curvature of all navigation Finsler metrics of isotropic S-curvature on Gaussian shrinking soliton.展开更多
文摘We show that on a Sasakian 3-sphere the Sasaki-Ricci flow initiating from a Sasakian metric of positive transverse scalar curvature converges to a gradient Sasaki-Ricci soliton.We also show the existence and uniqueness of gradient Sasaki-Ricci soliton on each Sasakian 3-sphere.
基金supported by the NNSF of China(11071257)Science Foundation of China University of Petroleum,Beijingsupported by Science and Technology Research Projectof Heilongjiang Provincial Department of Education(12511412)
基金supported by the YSBR-001,the NSFC(12201597)research funds from USTC(University of Science and Technology of China)and CAS(Chinese Academy of Sciences)+2 种基金supported by the YSBR-001the NSFC(11971452,12026251)a research fund from USTC.
文摘This paper is the sequel to our study of heat kernel on Ricci shrinkers[29].In this paper,we improve many estimates in[29]and extend the recent progress of Bamler[2].In particular,we drop the compactness and curvature boundedness assumptions and show that the theory of F-convergence holds naturally on any Ricci flows induced by Ricci shrinkers.
基金Supported by the National Natural Science Foundation of China(11771020,12171005).
文摘In this paper,we study a class of Finsler metrics defined by a vector field on a gradient Ricci soliton.We obtain a necessary and sufficient condition for these Finsler metrics on a compact gradient Ricci soliton to be of isotropic S-curvature by establishing a new integral inequality.Then we determine the Ricci curvature of navigation Finsler metrics of isotropic S-curvature on a gradient Ricci soliton generalizing result only known in the case when such soliton is of Einstein type.As its application,we obtain the Ricci curvature of all navigation Finsler metrics of isotropic S-curvature on Gaussian shrinking soliton.
基金Supported by the National Natural Science Foundation of China(11371386)the European Union’s Seventh Framework Programme(FP7/2007-2013)under grant agreement(317721)
