ON PSEUDOSYMMETRY TYPE HYPERSURFACES OF SEMI-EUCLIDEAN SPACES Ⅰ

In this paper the authors investigate hypersurfaces M of a semi-Euclidean space Esn+1, n ≥ 4, satisfying (aC +βR). H ＝ LkQ(g, Hk), k ＝ 1,2,3. Using obtained results they show additional curvature properties of investigated hypersurfaces.     

ON A CURVATURE CHARACTERIZATION OF RICCI-PSEUDOSYMMETRIC HYPERSURFACES

The author presents a curvature characterization of Ricci-pseudosymmetric hypersurfaces in semi-Riemannian space forms Ns^n 1(c), n≥4.     

THE CLOSED CURVES ON POSITIVE-TYPE HYPERSURFACES AND THE PERIODS OF NONLINEAR OSCILLATIONS

本文在Ｒｎ＋１中定义了一类超曲面并讨论了其上闭测地线长度的下界以及Ｈａｍｉｌｔｏｎ系统的周期解的最小周期，这类超曲面比星形超曲面广泛，因而本文结论包含了文献〔１〕、〔２〕、〔３〕中的相应结论     

Kaehler流形的全脐实超曲面

给出了Ｋａｅｈｌｅｒ流形的全脐实超曲面的一个分类定理。     

极小超曲面上Laplace算子的谱

本文证明了单位球面Ｓ＾ｎ＋１中某些Ｃｌｉｆｆｏｒｄ超曲面，复射影空间和四元数射影空间中广ＹＱ ＬＩＦＦＯＲＤＦＨＶ ＭＡ ＤＭ Ｊ ＭＨ ＡＤＷ Ｈ Ｌａｐｌａｃｅ算子的谱唯一确定。     

THE GEOMETRY OF HYPERSURFACES IN A KAEHLER MANIFOLD

Let M be a complex analytic manifOld there is given a positive definite quadratic differentialform[1]dS2 = gjkdZJdZ* (1)where the Latin indices j, k take the values 1,2,' l n; 1, 2,' t n. Assume the Greek indices o, Ptake the value8 1,2,', n and.=. l cr if i= al = 1 cr if i= a, (2)t cr if i = cr.Assume now that the symmetric tensor gjk is selfadoint(see below Definitioll l), that is-- --gap = g95 = go0 = g9rr, (3)g.0 = gPcr = gap = g05. (4)and 8atisfiesgoP = gap = 0. (5)From the com…     

齐型空间上的一类积分算子

在齐型空间上讨论由分数次积分算子、奇异积分算子及ＢＭＯ函数所构成的几类Ｔｏｅｐｌｉｔｚ型算子的有界性．     

ON DIRICHLET TYPE SPACES AND α-BLOCH SPACES IN THE UNIT BALL OF Cn

In this paper, the authors study the inclusion relations between Dirichlet type spaces DT and α-Bloch spacesβα by means of higher radial derivative. The strictness and the best possibility of the inclusion relations are shown with constructive methods.Furthermore, they sharpen one of the results when T = n, which proves that a conjecture in [7] is true.     

ON STATIONARY HYPERSURFACES IN EUCLIDEAN SPACES

Some techniques in the Geometric Measure Theory are used to study the hypersurfaces in Euclidean spaces and some fundamental properties with this subject are discussed in this article.     

Dupin超曲面的主曲率的重数

作者证明了如下结果 :设M是空间形式的闭定向Dupin超曲面 ,其截面曲率为正 ,M至少有两个不同主曲率 .如果除最小 (或最大 )主曲率外 ,M的其余主曲率均为常数 ,则最小 (或最大 )主曲率的重数大于 2 .     

NEW SPECTRAL CHARACTERIZATIONS OF EXTREMAL HYPERSURFACES

Let M be a closed extremal hypersurface in Sn+1 with the same mean curva-ture of the Willmore torus Wm,n?m. We proved that if Specp(M)=Specp(Wm,n?m) for p=0, 1, 2, then M is Wm,m.     

常曲率空间与全脐点超曲面

<正> 最近,胡和生证明了如下的命题:如果黎曼空间 V_(n+1)容有三系相互直交的常曲率全测地超曲面,那末 V_(n+1)是常曲率的,而且这些超曲面的曲率都相等.本文的目的是把这里全测地的条件换成较广泛的全脐点条件而证明同一结果.设 V_(+1)的基本张量是 α_(αβ)(α,β=1,…,n+1),而且超曲面V_n~((1))的方程是     

EQUIFOCAL HYPERSURFACES IN SYMMETRIC SPACES EQUIFOCAL HYPERSURFACES IN SYMMETRIC SPACES

1. IntroductionBy [111, a hypersurface in a symmetric space is called equifocal if every normal geodesicperpendiculajr to it is closed of constant length, say l, and contains Zg focal points for somepositive integer g. This is a natural generalization of isoparametric hypersurfaces in sphereswhere the illteger g is the number of distinct principal curvatures. In this note we considerequifocal hypersurfaces in simply connected rank one symmetric spaces, i.e. the complexprojective space CP", th…     

四元双曲空间中的实超曲面

设M是四元双曲空间中的实超曲面,若M是Weingarten形状算子A相对于三个特定方向平行,则M是一个管状超曲面。     

Dirichlet型空间上Hankel算子和乘法算子

本文讨论了Dirichlet型空间上的再生核,并对Dirichlet型空间上乘法算子,Hankel算子和小Hankel算子的基本性质进行了研究,同时也给出了这些算子的有界性,紧性和Schatten理想的初步刻画。     

PLEMELJ FORMULA OF CAUCHY TYPE INTEGRAL ON STEIN MANIFOLDS

Let D be a bounded domain with piecewise C(1) smooth orientable boundary on Stein manifolds, and let Φ(z) be a Cauchy type integral with Bochner-Martinelli kernel Ω(ψv, -S, S) and Holder continuous density function ψ(ζ), the authors define a solid angular coefficient α(t) at the point t ∈(e)D, prove that there exist the interior and outer limit values Φ± (t) under the meaning of the Cauchy principal value, and obtain the more general Plemelj formula and jump formula.     

KKM TYPE THEOREMS AND COINCIDENCE THEOREMS ON L-CONVEX SPACES

Some KKM theorems and coincidence theorems involving admissible set-valued mappings and the set-valued mappings with compactly local intersection property are proved in L-convex spaces. As applications, some new fixed point theorems are obtained in L-convex spaces. These theorems improve and generalize many important known results in recent literature.     

小Bloch型空间上的加权复合算子

本文将刻划从小Bloch型空间β0p到β0q(0＜p,q＜∞)上加权复合算子Tψ,ψ的有界性和紧性.同时得到了Tψ,ψ是Bloch型空间βp到βq(p＞1,0≤q≤1)有界算子的充要条件以及Tψ,ψ是Bloch型空间βp到βq(0≤p,q＜∞)紧算子的充要条件.     

齐型空间上的一类积分算子

在齐型空间上讨论由分数次积分算子、奇异积分算子及BMO函数所构成的几类Toeplitz型算子的有界性.     

ASYMPTOTIC BEHAVIOR OF OPERATORS OF PROBABILISTIC TYPE IN L_p SPACES

ＡＳＹＭＰＴＯＴＩＣＢＥＨＡＶＩＯＲＯＦＯＰＥＲＡＴＯＲＳＯＦＰＲＯＢＡＢＩＬＩＳＴＩＣＴＹＰＥＩＮＬ_ｐＳＰＡＣＥＳ￥ＣＨＥＮＷＥＮＺＨＯＮＧ；ＣＵＩＺＨＥＮＬＵ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓＸｉａｍｅｎＵｎｉｖｅｒｓｉｔｙ，Ｘｉ?..