排序方式: 共有16条查询结果,搜索用时 31 毫秒
1.
The aim of this note is two-fold. First, we investigate the relations between the volume growth of a submanifold and its second fundamental form. In the second part, we discuss the relations between the index of some Schrödinger operators and the structure of a submanifold, and prove some one-end theorems. 相似文献
2.
Let M be an -dimensional closed orientable submanifold in an -dimensional space form . We obtain an optimal upper bound for the second eigenvalue of a class of elliptic operators on M defined by , where T is a general symmetric, positive definite and divergence-free -tensor on M. The upper bound is given in terms of an integration involving tr T and , where tr T is the trace of the tensor T and is a normal vector field associated with T and the second fundamental form A of M. Furthermore, we give the sufficient and necessary conditions when the upper bound is attained. Our main theorem can be viewed as an extension of the famous “Reilly inequality”. The operator can be regarded as a natural generalization of the well-known operator which is the linearized operator of the first variation of the -th mean curvature for hypersurfaces in a space form. As applications of our main theorem, we generalize the results of Grosjean [17] and Li–Wang [20] in codimension one to arbitrary codimension. 相似文献
3.
We study a complete noncompact submanifold Mn in a sphere Sn+p. We prove that there admit no nontrivial L2-harmonic 1-forms on M if the total curvature is bounded from above by a constant depending only on n. The gap theorem is a generalized version of Carron?s, Yun?s, Cavalcante?s and the first author?s results on submanifolds in Euclidean spaces and Seo?s result on submanifolds in hyperbolic space without the condition of minimality. 相似文献
4.
We obtain ‘universal’ inequalities for the eigenvalues of the Laplacian acting on differential forms of a Euclidean compact
submanifold. These inequalities generalize the Yang inequality concerning the eigenvalues of the Dirichlet Laplacian of a
bounded Euclidean domain.
相似文献
5.
Vincent Borrelli 《Journal of Geometry and Physics》1998,25(3-4):271-290
On every totally real submanifold Mn of
n, one can define a Maslov class analogous to the one defined for the Lagrangian submanifolds of
n. We define here a closed 1-form, expressed in terms of the extrinsic local geometric invariants of Mn and the complex structure of
n, whose cohomology class is the Maslov class of Mn. This generalizes to the totally real case, the result of Morvan (1981). This 1-form can still be defined if the ambient space
n is substituted by a Kahler manifold
, but it is not closed in general. However, we can build a variational problem on the space of totally real immersions, whose critical points are totally real submanifolds whose form defined above vanishes identically. In the case where
, we give a characterization and many examples of such submanifolds. Finally we study the second variation and prove a stability result for the critical submanifolds of a Kahler manifold with non-positive Ricci tensor. This extends the well-known results on Lagrangian submanifolds of 相似文献
6.
Sharief Deshmukh 《Annali di Matematica Pura ed Applicata》2008,187(1):59-65
In this paper we study the role of constant vector fields on a Euclidean space R
n+p
in shaping the geometry of its compact submanifolds. For an n-dimensional compact submanifold M of the Euclidean space R
n+p
with mean curvature vector field H and a constant vector field on R
n+p
, the smooth function is used to obtain a characterization of sphere among compact submanifolds of positive Ricci curvature (cf. main Theorem).
相似文献
7.
首先详细地讨论了非紧Lie群的度量和Cartan分解,然后由Lie群和对称空间的关系得到了非紧对称空间中的子流形焦点存在的充要条件,同时还给出了焦点重数的计算方法. 相似文献
8.
This article gives some geometric inequalities for a submanifold with parallel second fundamental form in a pinched Riemannian manifold and the distribution for the square norm of its second fundamental form. 相似文献
9.
In this paper we mainly investigate projectively flat complete Kaehler sub-manifolds, in CPn. We give the pinching constants and the local structure. 相似文献
10.
Stefano Pigola 《Journal of Functional Analysis》2005,229(2):424-461
A general Liouville-type result and a corresponding vanishing theorem are proved under minimal regularity assumptions. The latter is then applied to conformal deformations of stable minimal hypersurfaces, to the L2 cohomology of complete manifolds, to harmonic maps under various geometric assumptions, and to the topology of submanifolds of Cartan-Hadamard spaces with controlled extrinsic geometry. 相似文献