Ricci Curvature of Certain Submanifolds in Kenmotsu Space Forms

In this paper, we obtain some sharp inequalities between the Ricci cur- vature and the squared mean curvature for bi-slant and semi-slant submanifolds in Kenmotsu space forms. Estimates of the scalar curvature and the k-Ricci curvature, in terms of the squared mean curvature, are also proved respectively.     

空间形式中常数量率的子流形

本文利用一个类似于Cheng和Yau引进的微分算子的新微分算子，得到了单位球面中常数量率的紧致子流形的一个刚性结果．     

余辛流形的半不变子流形的Ricci曲率

本文研究了余辛流形的半不变子流形,得到了这类子流形的Ricci曲率与平均曲率平方之间的—个不等式,并讨论了等式成立的充分必要条件．     

Finsler流形上的Laplace算子

该文对Finsler流形上的微分式定义了整体内积，进而引入δ算子和Laplace算子。该文还给出了δ算子的局部坐标表达式并且证明了Laplace算子可以看成是Riemann流形上Laplace算子在Finsler流形上的扩张。     

欧氏空间中完备极小子流形

在一个类似于稳定不等式的条件下,得到了欧氏空间中完备极小子流形的Bernstein型定理.我们的结果部分推广了Li H.Z.和Wei G.X.的定理.     

Totally Real Submanifolds in a Quaternion Space Form

In this paper, we prove a theorem for n-dimensional totally real minimal submanifold immersed in quaternion space form.     

阶化 Cartan 型李超代数的结合型

本文确定了具有非退化结合型的Ｃａｒｔａｎ型李超代数。     

关于(C~)循环空间中的脐子流形

本文讨论(C~)循环空间中的全脐子流形,证明了该子流形成为射影平坦或共圆平坦的充分必要条件是它又是爱因斯坦空间,这一结果推广了[1,2]中的相应结论.     

复射影空间的等参子流形

本文给出了复射影空间Ｐ＿ｎ（Ｃ）上的等参映射定义，并证明了等参映射ｆ在Ｈｏｐｆ主丛π：Ｓ￣（２ｎ＋１）→Ｐ＿ｎ（Ｃ）下的水平提升为Ｓ￣（２ｎ＋１）的等参映射。同时，利用对称空间的表示给出了Ｐ＿ｎ（Ｃ）上等参子流形的例子．     

双曲空间Hn+p(-1)中具常数量曲率的完备子流形

设Mn是Hn p(-1)中具有常标准数量曲率的n维完备子流形,本文证明了这种完备子流形的某些内蕴刚性定理和分类定理,并对超曲面的情形进行了研究．     

复射影空间的2-调和全实子流形

研究了复射影空间中2-调和全实子流形,得到了这类子流形的一个积分公式,讨论了伪脐条件下的情形,通过计算第二基本形式模长平方的Laplacian得到一个刚性定理.     

de Sitter空间中具平行平均曲率向量的完备类空子流形

本文证明了ｄｅＳｉｔｔｅｒ空间中具平行平均曲率向量的完备类空子流形在Ｈ２〉Ｃ时其第二基本形式模长平方是上有界的，从而推广了Ｕ－ＨａｎｇＫＩ＾（４）及Ｑ．Ｍ．Ｃｈｅｎｇ＾（３）中的结果。     

Contact CR-Warped Product Submanifolds in Sasakian Space Forms

Recently, B.-Y. Chen studied warped products which are CR-submanifolds in Kaehler manifolds and established general sharp inequalities for CR-warped products in Kaehler manifolds. Afterwards, I. Hasegawa and the present author obtained a sharp inequality for the squared norm of the second fundamental form (an extrinsic invariant) in terms of the warping function for contact CR-warped products isometrically immersed in Sasakian manifolds. In this paper, we improve the above inequality for contact CR-warped products in Sasakian space forms. Some applications are derived. A classification of contact CR-warped products in spheres, which satisfy the equality case, identically, is given.Mathematics Subject Classifications (2000). 53C40, 53C25.     

余辛空间形式中的子流形不等式

For submanifolds in a cosymplectic space form tangent to the structure vector field ξ, two important inequalities with Ricci curvature, scalar curvature and the squared mean curvature are obtained. These results are also applied to get corresponding consequences for anti-invariant submanifolds.     

Complete Space－like Submanifolds in a de Sitter Space with Parallel Mean CurvatureVector

ＣｏｍｐｌｅｔｅＳｐａｃｅ－ｌｉｋｅＳｕｂｍａｎｉｆｏｌｄｓｉｎａｄｅＳｉｔｔｅｒＳｐａｃｅｗｉｔｈＰａｒａｌｌｅｌＭｅａｎＣｕｒｖａｔｕｒｅＶｅｃｔｏｒＳｈｕＳｈｉｃｈａｎｇ（ＸｉａｎｙａｎｇＴｅａｃｈｅｒｓＣｏｌｌｅｇｅ，Ｘｉａｎｙａｎｇ，７１２...     

Ribaucour Transformations for Hypersurfaces in Space Forms

The theory of Ribaucour transformations for hypersurfaces in space forms is established. For any such hypersurface M, that admits orthonormal principal vector fields, it was shown the existence of a totally umbilic hypersurface locally associated to M by a Ribaucour transformation. A method of obtaining linear Weingarten surfaces in a three-dimensional space form is provided. By applying the theory, a new one-parameter family of complete constant mean curvature (cmc) surfaces in the unit sphere, locally associated to the flat torus, is obtained. The family contains a class of complete cmc cylinders in the sphere. In particular, one gets a family of complete minimal surfaces and minimal cylinders, locally associated to the Clifford torus.Mathematics Subject Classifications (2000): 53C20.     

Cartan矩阵,分解数与单模的顶

设Ｂ是有限群Ｇ的ｐ－块代数，考虑以Ｂ的Ｂｒａｕｅｒ不可约特征标为基底生成的自由Ａｂｅｌ群，以及由Ｂ的Ｃａｒｔａｎ矩阵决定的这个群的商群．通过研究这个商群中元素的阶数，我们得到了Ｃａｒｔａｎ矩阵和Ｃａｒｔａｎ数与单模的顶点及亏群的一些新关系式．对于常不可约特征标的高度，　我们得到了它与分解数以及Ｃａｒｔａｎ不变量的一些新关系式．     

de Sitter空间中法联络平坦的完备类空子流形

该文证明了de Sitter空间中具有平行平均曲率向量的常数量曲率完备类空子流形,如果其法联络是平坦的,且M的截面曲率小于0,或M的第二基本形式模长平方‖σ‖相似文献   

Sasakian流形中反不变极小子流形的稳定性

本文给出了Ｓａｓａｋｉａｎ流形中反不变极小子流形是稳定或不稳定的一个充分条件．