In this paper,it is proved that the Sasakian anti-holomorphic submanifolds of a Kaehlerian manifold is characterized by D-totally umbilical,and some curvature properties of the CR-submanifolds are ohtained.
We introduce and study a geometric heat flow to find Killing vector fields on closed Riemannian manifolds with positive sectional curvature. We study its various properties, prove the global existence of the solution ...We introduce and study a geometric heat flow to find Killing vector fields on closed Riemannian manifolds with positive sectional curvature. We study its various properties, prove the global existence of the solution to this flow, discuss its convergence and possible applications, and its relation to the Navier-Stokes equations on manifolds and Kazdan-Warner-Bourguignon-Ezin identity for conformal Killing vector fields. We also provide two new criterions on the existence of Killing vector fields. A similar flow to finding holomorphic vector fields on K¨ahler manifolds will be studied by Li and Liu(2014).展开更多
Let KD（z, z） be the Bergman kernel of a bounded domain 7P in Cn and Sect （z, ） and Ricci （z, ） be the holomorphic sectional curvature and Ricci curvature of the Bergman metric ds2 = T T：）（z,N）dzCdz respectiv...Let KD（z, z） be the Bergman kernel of a bounded domain 7P in Cn and Sect （z, ） and Ricci （z, ） be the holomorphic sectional curvature and Ricci curvature of the Bergman metric ds2 = T T：）（z,N）dzCdz respectively at the point z E T with tangent vector . It is proved by constructing suitable minimal functions that where z ∈D1 D D2, D1 is a ball contained in D and D2 is a ball containing D.展开更多
In this paper, the Laplacian on the holomorphic tangent bundle T 1,0 M of a complex manifold M endowed with a strongly pseudoconvex complex Finsler metric is defined and its explicit expression is obtained by using th...In this paper, the Laplacian on the holomorphic tangent bundle T 1,0 M of a complex manifold M endowed with a strongly pseudoconvex complex Finsler metric is defined and its explicit expression is obtained by using the Chern Finsler connection associated with (M, F ). Utilizing the initiated "Bochner technique", a vanishing theorem for vector fields on the holomorphic tangent bundle T 1,0 M is obtained.展开更多
文摘In this paper,it is proved that the Sasakian anti-holomorphic submanifolds of a Kaehlerian manifold is characterized by D-totally umbilical,and some curvature properties of the CR-submanifolds are ohtained.
基金supported by National Natural Science Foundation of China(Grant No.11401374)Shanghai YangFan Project(Grant No.14YF1401400)
文摘We introduce and study a geometric heat flow to find Killing vector fields on closed Riemannian manifolds with positive sectional curvature. We study its various properties, prove the global existence of the solution to this flow, discuss its convergence and possible applications, and its relation to the Navier-Stokes equations on manifolds and Kazdan-Warner-Bourguignon-Ezin identity for conformal Killing vector fields. We also provide two new criterions on the existence of Killing vector fields. A similar flow to finding holomorphic vector fields on K¨ahler manifolds will be studied by Li and Liu(2014).
基金supported by National Natural Science Foundation of China(Grant Nos.10671194 and 10731080/A01010501)
文摘Let KD（z, z） be the Bergman kernel of a bounded domain 7P in Cn and Sect （z, ） and Ricci （z, ） be the holomorphic sectional curvature and Ricci curvature of the Bergman metric ds2 = T T：）（z,N）dzCdz respectively at the point z E T with tangent vector . It is proved by constructing suitable minimal functions that where z ∈D1 D D2, D1 is a ball contained in D and D2 is a ball containing D.
基金Project Supported by the National Natural Science Foundation of China (Nos. 10871145, 10771174)the Doctoral Program Foundation of the Ministry of Education of China (No. 2009007Q110053)
文摘In this paper, the Laplacian on the holomorphic tangent bundle T 1,0 M of a complex manifold M endowed with a strongly pseudoconvex complex Finsler metric is defined and its explicit expression is obtained by using the Chern Finsler connection associated with (M, F ). Utilizing the initiated "Bochner technique", a vanishing theorem for vector fields on the holomorphic tangent bundle T 1,0 M is obtained.
