Goldberg and Wu studied a conformally flat manifold M with constant scalar curvature. When the Ricci curvature of M is of bounded below or positive,the conditions of M becoming a constant curvature manifold are obtain...Goldberg and Wu studied a conformally flat manifold M with constant scalar curvature. When the Ricci curvature of M is of bounded below or positive,the conditions of M becoming a constant curvature manifold are obtained. In this paper,we consider conharmonically flat manifolds and quasi conformally flat manifolds with constant saclar curvature. The corresponding results are generalized.展开更多
The notion of finite type submanifolds was introduced by B. Y. Chen. In this paper the conjectures on scalar curvature of Veronese generating submanifolds in E~σ and the minimal conjecture on Veronese space-like subm...The notion of finite type submanifolds was introduced by B. Y. Chen. In this paper the conjectures on scalar curvature of Veronese generating submanifolds in E~σ and the minimal conjecture on Veronese space-like submanifold Σ and Veronese pseudo-Riemannian submanifold in E_1~σ are proved. We have Σ is minimal in H^5. is minimal in S_1~5, Σ and are of 1-type in E_1~σ.展开更多
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.
In this paper, the authors construct a class of unitary invariant strongly pseudoconvex complex Finsler metrics which are of the form F =√[ rf(s- t)[, where r = ||v||~ 2, s =| z,v |~2/r, t =|| z||~ 2, f(w) is a real-...In this paper, the authors construct a class of unitary invariant strongly pseudoconvex complex Finsler metrics which are of the form F =√[ rf(s- t)[, where r = ||v||~ 2, s =| z,v |~2/r, t =|| z||~ 2, f(w) is a real-valued smooth positive function of w ∈ R,and z is in a unitary invariant domain M C^n. Complex Finsler metrics of this form are unitary invariant. We prove that F is a class of weakly complex Berwald metrics whose holomorphic curvature and Ricci scalar curvature vanish identically and are independent of the choice of the function f. Under initial value conditions on f and its derivative f, we prove that all the real geodesics of F =√[rf(s- t)] on every Euclidean sphere S^(2n-1) M are great circles.展开更多
文摘Goldberg and Wu studied a conformally flat manifold M with constant scalar curvature. When the Ricci curvature of M is of bounded below or positive,the conditions of M becoming a constant curvature manifold are obtained. In this paper,we consider conharmonically flat manifolds and quasi conformally flat manifolds with constant saclar curvature. The corresponding results are generalized.
基金Supported by the NSF of Henan Province Educ Dept(20021100002)Supported by the NSF of Henan Province Edu Dept(200510475038)
文摘In this paper we mainly investigate projectively flat complete Kaehler submanifolds, in CP^n. We give the pinching constants and the local structure.
文摘The notion of finite type submanifolds was introduced by B. Y. Chen. In this paper the conjectures on scalar curvature of Veronese generating submanifolds in E~σ and the minimal conjecture on Veronese space-like submanifold Σ and Veronese pseudo-Riemannian submanifold in E_1~σ are proved. We have Σ is minimal in H^5. is minimal in S_1~5, Σ and are of 1-type in E_1~σ.
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 the National Natural Science Foundation of China(Nos.11271304,11171277)the Program for New Century Excellent Talents in University(No.NCET-13-0510)+1 种基金the Fujian Province Natural Science Funds for Distinguished Young Scholars(No.2013J06001)the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry
文摘In this paper, the authors construct a class of unitary invariant strongly pseudoconvex complex Finsler metrics which are of the form F =√[ rf(s- t)[, where r = ||v||~ 2, s =| z,v |~2/r, t =|| z||~ 2, f(w) is a real-valued smooth positive function of w ∈ R,and z is in a unitary invariant domain M C^n. Complex Finsler metrics of this form are unitary invariant. We prove that F is a class of weakly complex Berwald metrics whose holomorphic curvature and Ricci scalar curvature vanish identically and are independent of the choice of the function f. Under initial value conditions on f and its derivative f, we prove that all the real geodesics of F =√[rf(s- t)] on every Euclidean sphere S^(2n-1) M are great circles.
