2型球面超曲面

本文证明了2型球面紧致超曲面具有常纯量曲率和常平均曲率，因而是质量对称的．     

Lorentz空间中常平均曲率类空超曲面

本文证明了ｎ＋１维Ｌｏｒｅｎｔｚ空Ｌｎ＋１中以Ｓｎ－１（ｒ）为边界的紧致常平均曲率类空超曲面只有 Ｂｎ（ｒ）和超伪球面盖．对于 Ｒｎ＋１中的紧致常平均曲率超曲面，当高斯映照像落在一个半球面内时，得到相应的唯一性结果．     

de Sitter空间中的类空超曲面在平均曲率下的形变

本文考虑了deSitter空间中紧致的类空扭曲面在平均曲率下的形变,证明了如果初始曲面满足某一Pinching条件,超曲面将收敛到一个球面．这一结论类似于球面上超曲面的情形,而与欧氏空间中的超曲面完全不同．     

Lorentz空间型中具有常数量曲率类空超曲面

研究了Lorentz空间型中具有常数量曲率的紧致类空超曲面,得到了这类超曲面的内蕴刚性定理.     

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.     

De Sitter空间中紧致类空超曲面的积分公式及其Goddard猜想的应用

本文对ｄｅＳｉｔｅｒ空间Ｓｎ＋１１（１）中紧致类空超曲面建立Ｍｉｎｋｏｗｓｋｉ型公式，并给出其到ｒ－次（ｒ＝１，２，…，ｎ－１）平均曲率为常数超曲面的应用．当ｒ＝１时，我们得到Ｍｏｎｔｉｅｌ的结果．     

球面上紧超曲面的等谱问题

本文讨论了球面上全脐超曲面与全测地超曲面的等谱问题。     

关于具有常平均曲率的超曲面

以N表示其截面曲率KN满足a≤KN≤b的n＋1维单连通完备黎曼流形，Mn是Nn 1中具有常平均曲率的紧致超曲面，本文给出了这类超曲面关于其第二基本形式模长平方S的积分不等式及相应的刚性定理．     

正定型超曲面上双曲闭特征的Maslov型指标的迭代公式

本文给出了R~(2n)中规范正定型超曲面上双曲闭特征的Maslov型指标的迭代公式.结果包含了凸超曲面和星形超曲面上已有的相应结论。     

de Siteer空间中拟紧致超曲面的一个全脐条件

在这篇文章中，讨论了具有常数量曲率的拟紧致超曲面，并给出了它是全脐子流形的一个全脐条件。     

Finite Type Non—Minimal Submanifolds

The notion of finite type xubmanifolds was introduced by B.Y.Chen.In this paper we consider the characteristics and the classifications of finite type non-minimal submanifolds.The characteristic theorems of 2-type Chen submanifolds、mass-symmetric hypersurfaces and Dupin hypersurfaces in Es^m are obtained.The classification theorems of 3-type hypersurfaces and null 2-type curves in Es^m are also proved.     

θ-型Calderón-Zygmund算子多线性交换子的加权估计

讨论了θ-型Calderón-Zygmund算子T与b=(b_1,b_2,…,b_m)(b_j∈Osc_(exp L~Tj),1≤j≤m)生成的多线性交换子(?)的加权估计.当0相似文献   

Low-type submanifolds of real space forms via the immersions by projectors

We undertake a comprehensive study of submanifolds of low Chen-type (1, 2, or 3) in non-flat real space forms, immersed into a suitable (pseudo) Euclidean space of symmetric matrices by projection operators. Some previous results for submanifolds of the unit sphere (obtained in [A. Ros, Eigenvalue inequalities for minimal submanifolds and P-manifolds, Math. Z. 187 (1984) 393–404; M. Barros, B.Y. Chen, Spherical submanifolds which are of 2-type via the second standard immersion of the sphere, Nagoya Math. J. 108 (1987) 77–91; I. Dimitrić, Spherical hypersurfaces with low type quadric representation, Tokyo J. Math. 13 (1990) 469–492; J.T. Lu, Hypersurfaces of a sphere with 3-type quadric representation, Kodai Math. J. 17 (1994) 290–298]) are generalized and extended to real projective and hyperbolic spaces as well as to the sphere. In particular, we give a characterization of 2-type submanifolds of these space forms with parallel mean curvature vector. We classify 2-type hypersurfaces in these spaces and give two sets of necessary conditions for a minimal hypersurface to be of 3-type and for a hypersurface with constant mean curvature to be mass-symmetric and of 3-type. These conditions are then used to classify such hypersurfaces of dimension n5. For example, the complete minimal hypersurfaces of the unit sphere Sⁿ⁺¹ which are of 3-type via the immersion by projectors are exactly the 3-dimensional Cartan minimal hypersurface and the Clifford minimal hypersurfaces M_k,n−k for n≠2k. An interesting characterization of horospheres in is also obtained.     

Spherical 2-type hypersurfaces

A hypersurface (not necessarily compact) of a hypersphereS ⁿ⁺¹ of a Euclidean spaceE ⁿ⁺² is of 2-type if and only if it has constant nonzero mean curvature inS ⁿ⁺¹ and constant scalar curvature, unless it is a portion of a small hypersphere inS ⁿ⁺¹. This shows that the 2-type compact hypersurfaces of a hypersphere are mass-symmetric.     

Non-embeddable real algebraic hypersurfaces

We study various classes of real hypersurfaces that are not embeddable into more special hypersurfaces in higher dimension, such as spheres, real algebraic compact strongly pseudoconvex hypersurfaces or compact pseudoconvex hypersurfaces of finite type. We conclude by stating some open problems.     

The Geometry of Lightlike Hypersurfaces of the de Sitter Space

It is proved that the geometry of lightlike hypersurfaces of the de Sitter space Sn+11 is directly connected with the geometry of hypersurfaces of the conformal space Cn. This connection is applied for a construction of an invariant normalization and an invariant affine connection of lightlike hypersurfaces as well as for studying singularities of lightlike hypersurfaces.     

Anisotropic isoparametric hypersurfaces in Euclidean spaces

In this paper, by Nomizu’s method and some technical treatment of the asymmetry of the F-Weingarten operator, we obtain a classification of complete anisotropic isoparametric hypersurfaces, i.e., hypersurfaces with constant anisotropic principal curvatures, in Euclidean spaces, which is a generalization of the classical case for isoparametric hypersurfaces in Euclidean spaces. On the other hand, by an example of local anisotropic isoparametric surface constructed by B. Palmer, we find that in general anisotropic isoparametric hypersurfaces have both local and global aspects as in the theory of proper Dupin hypersurfaces, which differs from classical isoparametric hypersurfaces.     

Boundary Problems for Dirac-Type Operators on Manifolds with Multi-Cylindrical End Boundaries

The goal of this paper is to establish a geometric program to study elliptic pseudodifferential boundary problems which arise naturally under cutting and pasting of geometric and spectral invariants of Dirac-type operators on manifolds with corners endowed with multi-cylindrical, or b-type, metrics and ‘b-admissible’ partitioning hypersurfaces. We show that the Cauchy data space of a Dirac operator on such a manifold is Lagrangian for the self-adjoint case, the corresponding Calderón projector is a b-pseudodifferential operator of order 0, characterize Fredholmness, prove relative index formulæ, and solve the Bojarski conjecture. Mathematics Subject Classifications (2000): 58J28, 58J52.     

On Submanifolds with 2-Type Pseudo-Hyperbolic Gauss Map in Pseudo-Hyperbolic Space

In this paper, we study pseudo-Riemannian submanifolds of a pseudo-hyperbolic space \(\mathbb H^{m-1}_s (-1) \subset \mathbb E^m_{s+1}\) with 2-type pseudo-hyperbolic Gauss map. We give a characterization of proper pseudo-Riemannian hypersurfaces in \(\mathbb H^{n+1}_s (-1) \subset \mathbb E^{n+2}_{s+1}\) with non-zero constant mean curvature and 2-type pseudo-hyperbolic Gauss map. For \(n=2\), we prove classification theorems. In addition, we show that the hyperbolic Veronese surface is the only maximal surface fully lying in \(\mathbb H^4_2 (-1) \subset \mathbb H^{m-1}_2 (-1)\) with 2-type pseudo-hyperbolic Gauss map. Moreover, we prove that a flat totally umbilical pseudo-Riemannian hypersurface \(M^n_t\) of the pseudo-hyperbolic space \(\mathbb {H}^{n+1}_t(-1) \subset \mathbb E^{n+2}_{t+1}\) has biharmonic pseudo-hyperbolic Gauss map.     

Lightlike Hypersurfaces of a Golden Semi-Riemannian Manifold

We introduce lightlike hypersurfaces of a golden semi-Riemannian manifold. We investigate several properties of lightlike hypersurfaces of a golden semi-Riemannian manifold. We prove that there is no radical anti-invariant lightlike hypersurface of a golden semi-Riemannian manifold. In particular, we obtain some results for screen semi-invariant lightlike hypersurfaces of a golden semi-Riemannian manifold. Moreover, we study screen conformal screen semi-invariant lightlike hypersurfaces.