Approximation of Schrödinger operators with δ‐interactions supported on hypersurfaces

We show that a Schrödinger operator with a δ‐interaction of strength α supported on a bounded or unbounded C²‐hypersurface , can be approximated in the norm resolvent sense by a family of Hamiltonians with suitably scaled regular potentials. The differential operator with a singular interaction is regarded as a self‐adjoint realization of the formal differential expression , where is an arbitrary bounded measurable function. We discuss also some spectral consequences of this approximation result.     

Pseudo‐Einstein real hypersurfaces in the complex quadric

In this article, we introduce the notion of pseudo‐Einstein real hypersurfaces in the complex quadric and give a complete classification of such hypersurfaces.     

单位球面Sn+1(1)中具有常平均曲率的超曲面

利用流形的紧致性,研究了单位球面Sn+1(1)中具有常平均曲率的紧致超曲面上的Schrodinger算子,讨论了此算子的最小特征值与子流形结构之间的联系,并得到了相应的定理,证明过程比相关文献更简单.     

Extrinsic Bounds for Eigenvalues of the Dirac Operator

We derive upper eigenvalue bounds for the Dirac operator of a closed hypersurface in a manifold with Killing spinors such as Euclidean space, spheres or hyperbolic space. The bounds involve the Willmore functional. Relations with the Willmore inequality are briefly discussed. In higher codimension we obtain bounds on the eigenvalues of the Dirac operator of the submanifold twisted with the spinor bundle of the normal bundle.     

A Parametrization of Isometric Immersions between Hyperbolic Spaces

We parametrize the space of isometric immersions of the hyperbolic n -space into the hyperbolic ( n +1)-space by a family of properly chosen (at most) countable n -tuples of real-valued functions. This is an answer to the problem posed by Nomizu in 1973. We also construct a one-parameter family of deformable isometric immersions from the quotient spaces of the hyperbolic 2-plane modulo and some totally discontinuous subgroups of isometries.     

Characterization of totally umbilic hypersurfaces in a space form by circles

In this paper we characterize totally umbilic hypersurfaces in a space form by a property of the extrinsic shape of circles on hypersurfaces. This characterization corresponds to characterizations of isoparametric hypersurfaces in a space form by properties of the extrinsic shape of geodesics due to Kimura-Maeda.The first author was partially supported by Grant-in-Aid for Scientific Research (C) No. 14540075, Ministry of Education, Science, Sports and Culture. The second author was partially supported by Grant-in-Aid for Scientific Research (C) No. 14540080, Ministry of Education, Science, Sports and Culture.     

Conformally Flat Semi-Riemannian Manifolds with Nilpotent Ricci Operators and Affine Differential Geometry

We investigate the conformally flat semi-Riemannian manifolds withnilpotent Ricci operators. We construct a lot of complete orhomogeneous, conformally flat semi-Riemannian manifolds with nilpotentRicci operators. In this construction, we show interesting relationsbetween the semi-Riemannian geometry and the affine differentialgeometry of centro-affine hypersurfaces.     

Integral formulas for compact spacelike hypersurfaces in de sitter space and their applications to Goddard's conjecture

We establish integral formulas of Minkowski's type for compact spacelike hypersurfaces in de sitter spaceS ₁ ⁿ⁺¹ (1) and give their applications to the case of constantr-th mean curvature (r=1,2,…,n−1). Whenr=1 we recover Montiel's result. Li Haizhong is supported by NNSFC No.19701017 and Basic Science Research Foundation of Tsinghua University and Chen Weihua is supported by NNSFC No. 19571005