共查询到15条相似文献,搜索用时 0 毫秒
1.
We study manifolds where the natural skew-symmetric curvature operator has pointwise constant eigenvalues. We give a local classification (up to isometry) of such manifolds in dimension 4. In dimension 3, we describe such manifolds up to a classification of three - dimensional Riemannian manifolds with principal Ricci curvatures r1 = r2 = 0, r3- arbitrary. We give examples of such manifolds in all dimensions which do not have constant sectional curvature; these manifolds are not pointwise Osserman manifolds in general. 相似文献
2.
拟常曲率黎曼流形中具有平行平均曲率向量的子流形 总被引:2,自引:0,他引:2
讨论了拟常曲黎曼流形中具有平行平均曲率向量的等距浸入子流形,给出了一个积分不等式,推广和改进献[1,2]的结果。 相似文献
3.
The complete space-like hypersurfaces with constant normal saclar curvature is discussed in a locally symmetric Lorentz space. A classified theorem is obtained by the operator L_1 introduced by S Y Cheng and S T Yau [3]. 相似文献
4.
V. S. Dryuma 《Theoretical and Mathematical Physics》2006,146(1):34-44
We construct some examples of three-dimensional metrics of constant curvature defined by the solutions of nonlinear integrable
differential equations and their generalizations and study the properties of Riemann extensions of the metrics of constant
curvature. We discuss the connection with the theory of normal Riemannian spaces.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 1, pp. 42–54, January, 2006. 相似文献
5.
Philippe Castillon 《Annals of Global Analysis and Geometry》1999,17(6):563-579
In this work we determine the essential spectrum of the stability operator of a submanifold of the hyperbolic space with constant mean curvature h < 1 and finite total curvature. In some particular cases, we also give a bound on the number of eigenvalues which are below the essential spectrum. 相似文献
6.
M. I. Cherdantsev 《Mathematical Notes》2005,78(1-2):270-278
In this paper, we consider eigenvalue problems for the Laplace operator in three-dimensional domains with singularly perturbed boundary. Perturbations are generated by a complementary Dirichlet boundary condition on a small nonclosed surface inside the domain. The convergence and the asymptotic behavior of simple eigenvalues of the problem are considered.__________Translated from Matematicheskie Zametki, vol. 78, no. 2, 2005, pp. 299–307.Original Russian Text Copyright © 2005 by M. I. Cherdantsev. 相似文献
7.
We study the global umbilic submanifolds with parallel mean curvature vector fields in a Riemannian manifold with quasi constant curvature and get a local pinching theorem about the length of the second fundamental form. 相似文献
8.
研究了拟常曲率流形中具有平行平均曲率向量的子流形,给出了两个积分不等式. 相似文献
9.
10.
常曲率空间中单形的某些条件极值问题 总被引:4,自引:0,他引:4
借助于矩阵次特征值的概念,建立了线性约束二次型正定的一个充分必要条件,给出了常曲率空间中单形外接超球半径的某些条件极值表示,由此可以导出了一些“度量加”的几何不等式. 相似文献
11.
Jorge Herbert S. de Lira 《Annals of Global Analysis and Geometry》2002,21(2):123-133
It is proved that an embedded hypersurface in a hemisphere of the Euclidean unit spherewith constant mean curvature and spherical boundary inherits, under certainconditions, the symmetries of its boundary. In particular, spherical caps are theonly such hypersurfaces whose boundary are geodesic spheres. 相似文献
12.
常曲率空间中共球有限点集的一类几何不等式 总被引:6,自引:0,他引:6
本文首先证明了一个代数不等式,其次利用它得到了n维常曲率空间中共球有限点集的一类几何不等式,其特殊情况得到了文[3]中的主要结论. 相似文献
13.
Yu. V. Volodin 《Mathematical Notes》2006,79(1-2):185-195
We establish sufficient conditions for the absence of global solutions of the differential inequality Δ2 u≥|u|q in the exterior of a ball. We consider various boundary conditions and show that the critical exponents depend on these conditions. The proofs are based on the test function method developed by Mitidieri and Pokhozhaev. 相似文献
14.
15.
XuSenlin ChenDongmei 《分析论及其应用》2004,20(4):383-390
The purpose of this paper is to study complete space-like submanifolds with parallel mean curvature vector and flat normal bundle in a locally symmetric semi-defnite space satisfying some curvature conditions. We first give an optimal estimate of the Laplacian of the squared norm of the second fundamental form for such submanifold. Furthermore, the totally umbilical submanifolds are characterized 相似文献