1) Ricci principle curvature
Ricci主曲率
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) 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。
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。
补充资料：主曲率
主曲率
principal curvature
主曲率[州州间。.n.灿代;rJI~aa冲.洲3朋] 曲面沿主方向(沿使法曲率取极值的方向)的法曲率(norn笼11 cUr坡nu限).主曲率k.和k:是二次方程: }工一、EM一、尸 }M一kFN一kG的根，其中E，F和G是第一基本形式(阮tfu以加-1们眨ntalfo皿)的系数，而L，M和N是第二基本形式(second fondanrn‘d form)的系数，它们在给定点计值. 曲面主曲率k，和kZ之和的一半给出平均曲率(nlean cun傲t昵)，而它们的乘积等于曲面的C皿弥曲率(Gau资助以uv吐口限).方程(，)可写为 kZ一ZHk+K二O，其中H和K是曲面在给定点的平均曲率和C比u骆曲率. E山er公式(E司er fonnu」a): k=k、cosZ甲+人2 sinZ明，使主曲率k:和kZ与任意方向的法曲率k联系起来、其中甲是所选方向与火.的主方向作成的角. E .B .1肠以HH撰[补注1 在n维Eudjd空间E”的m维子流形M的情况下，主曲率和主方向定义如下. 设心是M在P任M处的单位法向量.M在p处沿方向亡的研触i侧势dell映射(W己山孚血n mapp雌)(攀攀纂于(s加pe ope.tor))A。由一砖的切向部分出，其中万是E”中的共变微分(co~ntd迁免代n-回)，七是由古局部延拓成的单位向量场.A;与所选的肯延拓无关.M在p处沿方向遭的主曲率由A;的特征值给出，主方向由它的特征方向给出.人的特征值的(规范化)初等对称函数定义了M的高阶平均曲率(1五gl℃rn犯an~t比re)，它包括作为极端情况的平均曲率(A;的迹)和LIPsc场tZ一幻伍嗯曲率(LIPschitZ一K沮ing culvat理沈)(它的行列式).
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