类拟的Euler公式

经典的欧拉公式描述了两曲面交线的曲率和曲面的法曲率以及曲面夹角之间的关系。本文给出了R3中曲面的法曲率的欧拉公式的简单证明。并得到一个关于曲面交线曲率及曲面测地曲率的类似的欧拉公式。     

中曲率大于零的非凸曲面

本文研究了曲面的曲率问题.利用积分几何方法和旋转曲面性质,构造出一个欧氏空间R3中紧致光滑的中曲率H大于零的非凸曲面,并得到了关于紧致光滑曲面曲率的几个不等式.     

Dirac-Witten算子特征值的下界估计

在某些条件下,我们获得了Lorentzian流形中紧致spin类空超曲面（无边或带边）的Dirac-Witten算子特征值的一个优化下界估计.该估计依赖于超曲面的数量曲率、平均曲率以及旋量诱导的能量动量张量.在极限情形下,我们发现类空超曲面或者是极大的且具有正数量曲率的Einstein流形,或者是具有非零常平均曲率的Ricci平坦流形.     

具有平行平均曲率向量子流形的曲率估计与稳定性

本文估计空间形式中具有平行平均曲率向量子流形上共形度量的数量曲率上界,并利用其研究了具有常平均曲率超曲面的稳定性．     

S^4（1）中具有常拟Gauss—Kronecker曲率的超曲面

给出了拟Gauss-Kronecker曲率的定义,并研究了S~4(1)中具有常拟Gauss-Kro-necker曲率的超曲面的特性。     

常平均曲率超曲面的曲率估计与稳定性

本文估计了空间形式Ｎ^ｎ＋１（ｃ）中常平均曲率超曲面上共形度量的曲率上界,并用其研究了Ｎ^ｎ＋１（ｃ）中常平均曲率超曲面的强稳定性．     

双三次Bézier曲面片的光滑拼接

本文根据曲面的总曲率和平均曲率推导出双三次Bézier曲面片拼接的C2连续条件.     

αK bH=c曲面的Bcklund变换

本文首先对Ｇａｕｓｓ曲率Ｋ和平均曲率Ｈ满足线性关系ａＫ＋ｂＨ＝ｃ的曲面，证明了其ＧａｕｓｓＷｅｉｎｇａｒｔｅｎ公式不仅可看作曲面的Ｇａｕｓｓ－Ｃｏｄａｚｚｉ方程的Ｌａｘ对，而且给出了Ｂ¨ａｃｋｌｕｎｄ变换．然后，将著名的关于负常曲率的Ｂ¨ａｃｋｌｕｎｄ定理推广到主曲率ｋ１和ｋ２满足关系（ｋ１－ｍ）（ｋ２－ｍ）＝－ｌ２的曲面     

常曲率空间的半平行超曲面和高阶平行超曲面的分类

本文给出了非欧氏常曲率空间Ｎ＾ｎ＋１（Ｃ）的半平行超曲面的分类，并利用此分类定理证明了非欧氏常曲率空间的高阶平行超曲面与平行超曲面的等价性，从而也给出了非欧氏常曲率空间的高阶平行超曲面的分类；     

宇宙时空中具有给定平均曲率的类空超曲面

本文研究了宇宙时空中类空超曲面的推广平均曲率流,通过估计发展超曲面的高度函数、梯度函数和曲率函数等几何量,得到了一类极限类空超曲面,其平均曲率等于给定函数.     

Properties of Berwald scalar curvature

We prove that a Finsler manifold with vanishing Berwald scalar curvature has zero E-curvature. As a consequence, Landsberg manifolds with vanishing Berwald scalar curvature are Berwald manifolds. For (α,β)-metrics on manifold of dimension greater than 2, if the mean Landsberg curvature and the Berwald scalar curvature both vanish, then the Berwald curvature also vanishes.     

Finsler metrics with special Riemannian curvature properties

The Weyl curvature is one of the fundamental quantities in Finsler geometry because it is a projective invariant. By determining the Weyl curvature of a class of Finsler metrics, we find a lot of Finsler metrics of quadratic Weyl curvature which are non-trivial in the sense that they are not of quadratic Riemann curvature.     

A Schur type lemma for the mean Berwald curvature in Finsler geometry

In this short paper, we study a symmetric covariant tensor in Finsler geometry, which is called the mean Berwald curvature. We first investigate the geometry of the fibres as the submanifolds of the tangent sphere bundle on a Finsler manifold. Then we prove that if the mean Berwald curvature is isotropic along fibres, then the Berwald scalar curvature is constant along fibres.     

A note on constant geodesic curvature curves on surfaces

In this paper we are concerned with the structure of curves on surfaces whose geodesic curvature is a large constant. We first discuss the relation between closed curves with large constant geodesic curvature and the critical points of Gauss curvature. Then, we consider the case where a curve with large constant geodesic curvature is immersed in a domain which does not contain any critical point of the Gauss curvature.     

有关法曲率的若干性质

以[2]中经典微分几何问题为切入点,运用复数与三角工具广泛深入地探讨了“过曲面上一点有n条切线,若相邻两条切线的交角为2nπ,曲面法线与切线所定平面截得曲线的曲率半径为ρ1,ρ2,ρ3,…,ρn时,∑ni=11ρim,∑ni=1ρi,∏ni=1ρi的结果”,得到了法曲率与相关的三个有趣定理.     

一类Reinhardt域的几何性质

讨论了一类Reinhardt域的几何性质，包括其Bergman度量、Ricci曲率、无向曲率及酉曲率。最后，还讨论了该域的面积定理。     

Complete hypersurfaces in a 4-dimensional hyperbolic space

This paper gives a classification of complete hypersurfaces with nonzero constant mean curvature and constant quasi-Gauss-Kronecker curvature in the hyperbolic space H4（-1）,whose scalar curvature is bounded from below.     

Finsler空间上的Weyl曲率

The Weyl curvature of a Finsler metric is investigated. This curvature constructed from Riemannain curvature. It is an important projective invariant of Finsler metrics. The author gives the necessary conditions on Weyl curvature for a Finsler metric to be Randers metric and presents examples of Randers metrics with non-scalar curvature. A global rigidity theorem for compact Finsler manifolds satisfying such conditions is proved. It is showed that for such a Finsler manifold,if Ricci scalar is negative,then Finsler metric is of Randers type.