1) bi-Ricci curvature
双Ricci曲率
1.
The paper shows that a complete, noncompact, oriented and strongly stable hypersurface M with constant mean curvature H in a (n+1)-dimensional complete oriented manifold N~(n+1) with bi-Ricci curvature,being not less than -n~2H~2 along M, admits no nontrivial L~2 harmonic 1-forms.
设M为(n+1)维流形N中完备、非紧、定向的、具有常平均曲率H的强稳定超曲面,文中证明了若N的双Ricci曲率沿M不小于-n2H2,则M上不存在非平凡的L2调和1-形式。
2) Ricci curvature
Ricci曲率
1.
A uniformation theorem on complete noncompactn-dimensional(m=2n) Khler manifold with nonnegative and bounded Ricci curvature is studied,if the conditoins as follow are satisfied:① section curvature kr(x0)≥-c/(1+r2);②‖f‖p≤ C0‖▽ f‖q,f∈C∞0(M),1≤q≤n,1/p=1/q-1/m;③ ∫_M Rnic<∞.
现得到完备非紧且Ricci曲率非负有界n维(m=2n)的Khler流形M上的一个单值化定理。
2.
Let M be an n(n≥3)-dimensional complete spacelike hypersurface in de Sitter space, S~n+11(1)with constant mean curvature H and constant scalar curvature, it also has nonegative Ricci curvature, then it is isometric to a sphere or an euclidean space or a hyperbolic cylinder.
设M为deSitter空间Sn+11(c)中的完备类空超曲面,具有常平均曲率向量和常数量曲率以及非负Ricci曲率,则它与球空间、欧氏空间或者双曲柱面等距。
3.
A property of certain harmonic maps of Ricci curvature which have positive low bound on compact Riemann manifolds,as well as the Eigenvalue estimation problem of harmonic maps are discussed,we get a condition that a harmonic maps is a totally geodesic map.
主要讨论Ricci曲率具有正下界的紧Rieman流形M上的调和映射 。
3) Ricci principle curvature
Ricci主曲率
4) Ricci-isotropic curvature
迷向Ricci曲率
5) Nonnegative Ricci curvature
非负Ricci曲率
1.
The topology of complete manifolds with nonnegative Ricci curvature and large volume growth;
具非负Ricci曲率和大体积增长的完备流形的拓扑(英文)
2.
For an open complete Riemannian manifold with nonnegative Ricci curvature,the present paper discusses the relation between the topology and the volume growth.
本文讨论了具非负Ricci曲率的完备非紧黎曼流形的体积增长与其拓扑性质之间的关系。
3.
By comparing the volume growth order of the manifold itself to that of its universal covering space, the paper proves that every three-dimensional with nonnegative Ricci curvature and (1+δ)-order volume growth in strict sense must be contractible provided that its universal covering is finite.
本文研究了三维完备非紧具非负Ricci曲率的黎曼流形的几何拓扑性质。
6) parallel Ricci curvature
平行Ricci曲率
1.
In this paper,we study the minimal submanifolds in a Riemannian manifolds with parallel Ricci curvature.
主要研究了具有平行Ricci曲率黎曼流形中的极小子流形,获得了J。
2.
In chapter 3,sectional curvature\'s Pinching of minimal submanifold in a Riemannian manifolds with parallel Ricci curvature is discussed, getting a Pinching theorems.
第三章研究了具有平行Ricci曲率黎曼流形中的极小子流形关于截面曲率的Pinching定理,推广了球面该类子流形的有关结果。
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