共查询到20条相似文献,搜索用时 93 毫秒
1.
本文把Berard P.,do Carmo M.,Santos W.在1998年所得的结果,分别推广到局部对称的Cartan-Hadamard流形中具有常平均曲率和有限全曲率的完备超曲面,以及球面上具有平行平均曲率和有限全曲率的完备子流形. 相似文献
2.
Since the induced objects on a lightlike submanifold depend on its screen distribution which, in general, is not unique and hence we can not use the classical submanifold theory on a lightlike submanifold in the usual way. Therefore, in present paper, we study screen conformal lightlike submanifolds of a semi-Riemannian manifold, which are essential for the existence of unique screen distribution. We obtain a characterization theorem for the existence of screen conformal lightlike submanifolds of a semi-Riemannian manifold. We prove that if the differential operator Ds is a metric Otsuki connection on transversal lightlike bundle for a screen conformal lightlike submanifold then semi-Riemannian manifold is a semi-Euclidean space. We also obtain some characterization theorems for a screen conformal totally umbilical lightlike submanifold of a semi-Riemannian space form. Further, we obtain a necessary and sufficient condition for a screen conformal lightlike submanifold of constant curvature to be a semi-Euclidean space. Finally, we prove that for an irrotational screen conformal lightlike submanifold of a semi-Riemannian space form, the induced Ricci tensor is symmetric and the null sectional curvature vanishes. 相似文献
3.
局部对称共形平坦黎曼流形中具有平行平均曲率向量的子流形 总被引:8,自引:0,他引:8
本文把[1]的结论推广到了环绕空间是局部对称共形平坦的情形,即获得了:设M~是局部对称共形平坦黎曼流形N~+p(p>1)中具有平行平均曲率向量的紧致子流形,如果则M~位于N~+p的全测地子流形N~+1中。其中S,H分别是M~的第二基本形式长度的平方和M~的平均曲率,T_C、t_c分别是N~+p的Ricci曲率的上、下确界,K是N~+p的数量曲率。 相似文献
4.
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
5.
We investigate the submanifold geometry of the orbits of Hermann actions on Riemannian symmetric spaces. After proving that
the curvature and shape operators of these orbits commute, we calculate the eigenvalues of the shape operators in terms of
the restricted roots. As applications, we get a formula for the volumes of the orbits and a new proof of a Weyl-type integration
formula for Hermann actions.
相似文献
6.
JianQuan Ge 《中国科学A辑(英文版)》2008,51(6):1127-1134
By using moving frame theory,first we introduce 2p-th mean curvatures and(2p 1)-th mean curvature vector fields for a submanifold.We then give an integral expression of them that characterizes them as mean values of symmetric functions of principle curvatures.Next we apply it to derive directly the celebrated Weyl-Gray tube formula in terms of integrals of the 2p-th mean curvatures and some Minkowski-type integral formulas. 相似文献
7.
Vladimir Rovenski 《Israel Journal of Mathematics》2007,159(1):289-316
We study the structure of the minimum set of the normal curvature for a symmetric bilinear map on Euclidean or Hilbert space,
the conditions when this set contains strongly umbilical, conformal nullity, etc. linear subspaces. The main goals are estimates
from above of the codimension of these subspaces for a symmetric bilinear map with positive normal curvature and the inequality
type restriction on the extrinsic qth scalar curvature. We estimate from above the codimension of asymptotic and relative nullity subspaces for a symmetric bilinear
map with nonpositive extrinsic qth scalar curvature.
Applying the algebraic results to the second fundamental form of a submanifold with low codimension, we characterize the totally
umbilical and totally geodesic submanifolds, prove local nonembedding theorems for the products of Riemannian manifolds and
global extremal theorem for the space of positive curvature. On the way we generalize results by Florit (1994), Borisenko
(1977, 1987) and Okrut (1991) about Riemannian and Hilbert submanifolds.
The research was supported by the Center for Absorption in Science, Ministry of Immigrant Absorption, State of Israel; and
by Center for Computational Mathematics and Scientific Computation, University of Haifa. 相似文献
8.
S. E. Kozlov 《Journal of Mathematical Sciences》2004,119(2):223-229
An infinitesimal criterion indicating when a two-dimensional submanifold of a Riemannian symmetric space is totally geodesic is given. As an application, the classification of two-dimensional totally geodesic submanifolds of the Grassmannian of bivectors is given in a new way, and it is proved that the sectional curvature takes stationary values on tangent spaces of such submanifolds. Bibliography: 9 titles. 相似文献
9.
本文首先将常曲率黎曼流形中B.Y.Chen和M.Okumura关于数量曲率和截面曲率关系间的一个著名不等式推广到环绕空间是局部对称共形平坦黎曼流形的情形.作为应用,较简捷地将M.Okumura在[2],[3]中的结果推广到这种环绕空间中法联络是平坦的子流形上去. 相似文献
10.
关于局部对称空间中的伪脐子流形 总被引:8,自引:0,他引:8
本文讨论了局部对称完备黎曼流形中的紧致伪脐子流形,且具有平行平均山率向量场。得到了这类子流形成为全脐子流形及其余维数减小的几个拼挤定理。 相似文献
11.
In this paper, we introduce and study the conformal mean curvature flow of submanifolds of higher codimension in the Euclidean space R~n. This kind of flow is a special case of a general modified mean curvature flow which is of various origination. As the main result, we prove a blow-up theorem concluding that, under the conformal mean curvature flow in R~n, the maximum of the square norm of the second fundamental form of any compact submanifold tends to infinity in finite time. Furthermore, we also prove that the external conformal forced mean curvature flow of a compact submanifold in R~n with the same pinched condition as Andrews-Baker's will be convergent to a round point in finite time. 相似文献
12.
This paper gives some sufficient conditions for a compact Kaehler submanifold M~n in a locally symmetric Bochner-Kaehler manifold ~(n p) to be totally geodesic. The conditions are given by inequalities which are established between. the sectional curvature(resp, holomorphic sectional curvature) of M~n and the Ricci curvature of ~(n p). In particular, similar results in the case where ~(n p) is a complex projective spathe are contained. 相似文献
13.
We prove that a Lagrangian submanifold passes through each point of a symplectic manifold in the direction of arbitrary Lagrangian plane at this point. Generally speaking, such a Lagrangian submanifold is not unique; nevertheless, the set of all such submanifolds in Hermitian extension of a symplectic manifold of dimension greater than 4 for arbitrary initial data contains a totally geodesic submanifold (which we call the s-Lagrangian submanifold) iff this symplectic manifold is a complex space form. We show that each Lagrangian submanifold in a complex space form of holomorphic sectional curvature equal to c is a space of constant curvature c/4. We apply these results to the geometry of principal toroidal bundles. 相似文献
14.
Heiko Ewert 《Proceedings of the American Mathematical Society》1998,126(8):2443-2452
A submanifold in a symmetric space is called equifocal if it has a globally flat abelian normal bundle and its focal data is invariant under normal parallel transportation. This is a generalization of the notion of isoparametric submanifolds in Euclidean spaces. To each equifocal submanifold, we can associate a Coxeter group, which is determined by the focal data at one point. In this paper we prove that an equifocal submanifold in a simply connected compact symmetric space is a non-trivial product of two such submanifolds if and only if its associated Coxeter group is decomposable. As a consequence, we get a similar splitting result for hyperpolar group actions on compact symmetric spaces. These results are an application of a splitting theorem for isoparametric submanifolds in Hilbert spaces by Heintze and Liu.
15.
A. A. Borisenko 《Mathematical Notes》1996,60(1):3-7
In this paper we consider compact multidimensional surfaces of nonpositive external curvature in a Riemannian space. If the
curvature of the underlying space is ≥ 1 and the curvature of the surface is ≤ 1, then in small codimension the surface is
a totally geodesic submanifold that is locally isometric to the sphere. Under stricter restrictions on the curvature of the
underlying space, the submanifold is globally isometric to the unit sphere.
Translated fromMatematicheskie Zametki, Vol. 60, No. 1, pp. 3–10, July, 1996. 相似文献
16.
Claudio Gorodski 《Proceedings of the American Mathematical Society》2004,132(8):2441-2447
We show that a totally geodesic submanifold of a symmetric space satisfying certain conditions admits an extension to a minimal submanifold of dimension one higher, and we apply this result to construct new examples of complete embedded minimal submanifolds in simply connected noncompact globally symmetric spaces.
17.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1998,326(3):335-338
On the unit ball of, one considers the standard hyperbolic metric H0 whose Ricci curvature equals R0 and Riemann-Christoffel curvature is. We prove that, for any symmetric tensor R near R0, there exists a unique metric H near H0 whose Ricci curvature is R. We deduce in the C∞ case that the image of the Riemann-Christoffel operator is a submanifold in a neighborhood of. Finally, we study more precisely the Ricci equation in dimension 2. 相似文献
18.
A topological sphere theorem is obtained from the point of view of submanifold geometry. An important scalar is defined by the mean curvature and the squared norm of the second fundamental form of an oriented complete submanifold Mn in a space form of nonnegative sectional curvature. If the infimum of this scalar is negative, we then prove that the Ricci curvature of Mn has a positive lower bound. Making use of the Lawson–Simons formula for the nonexistence of stable k-currents, we eliminate Hk (Mn, Z) for all 1 ` k ` n – 1.We then observe that the fundamental group of Mn is trivial. It should be emphasized that our result is optimal. 相似文献
19.
Shen yibing 《数学年刊B辑(英文版)》1984,5(4):625-632
This paper gives some sufficient conditions for a compact submanifold with nonnegative sectional curvature in a space form to be totally umbilical. In particular, for a compact submanifold M with flat normal bundle, if the scalar curvature is proportional to the mean curvature everywhere, then M is totally umbilical or the Riemannian product of several totally umbilical constantly curved submanifolds. 相似文献
20.
Jake P. Solomon 《Geometric And Functional Analysis》2014,24(2):670-689
A Lagrangian submanifold in an almost Calabi–Yau manifold is called positive if the real part of the holomorphic volume form restricted to it is positive. An exact isotopy class of positive Lagrangian submanifolds admits a natural Riemannian metric. We compute the Riemann curvature of this metric and show all sectional curvatures are non-positive. The motivation for our calculation comes from mirror symmetry. Roughly speaking, an exact isotopy class of positive Lagrangians corresponds under mirror symmetry to the space of Hermitian metrics on a holomorphic vector bundle. The latter space is an infinite-dimensional analog of the non-compact symmetric space dual to the unitary group, and thus has non-positive curvature. 相似文献