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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
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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
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得到了Cayley射影平面的全复浸入Kaehler曲面的一些有趣的拓扑限制。 相似文献
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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
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H一射影循环Kaehler流形 总被引:2,自引:0,他引:2
李中林 《浙江大学学报(理学版)》1994,21(1):16-19
本文研究H一射影循环Kaehler流形的性质,导出了该流形曲率张量的代数结构,从而深化了这类流形的已有结果。 相似文献
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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
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本文研究Coupled Vortex方程的Dirichlet问题,通过热流方法来讨论该方程Dirichlet问题的解的存在唯一性. 相似文献
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复射影空间CP^n+p的Kaehler子流形 总被引:2,自引:0,他引:2
本文对复射影空间CPn+p中具有非负全实双截面曲率的n维(p<n)紧致Kaehler子流形作了完全分类. 相似文献
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研究复射影空间的拟共形平坦Kaehler完备子流形得到局部结构与关于数量曲率的拼挤常数. 相似文献