局部对称拟常曲率黎曼流形中伪脐子流形的Pinching定理

讨论局部对称拟常曲率黎曼流形Nn+p中具有平行平均曲率向量的紧致伪脐子流形Mn,得到了Mn是全脐子流形的两个Pinching定理.     

拟常曲率黎曼流形中具有平行平均曲率向量的子流形

研究拟常曲率黎曼流形中具有平行平均曲率向量的紧致子流形. 通过计算子流形第二基本形式模长平方的拉普拉斯, 利用Stokes定理, 得到这类子流形的一个积分不等式. 使得对拟常曲率黎曼流形中紧致子流形的研究由极小子流形和伪脐子流形情形扩展到具有平行平均曲率向量的情形.     

平行Ricci曲率黎曼流形中具有平行中曲率向量的子流形

研究了具有平行Ricci曲率黎曼流形中具有平行中曲率向量的子流形.获得了J.8imons型积分不等式,推广了局部对称空间该类子流形的相关结果.     

伪黎曼流形中具有平行平均曲率向量的伪脐子流形

研究了伪黎曼流形中具有平行平均曲率向量的伪脐子流形,Npn p为n p维完备连通伪黎曼流形,它的截面曲率KN满足a≤KN≤b,Mn为Npn p中紧致的具有平行平均曲率向量的伪脐子流形.通过利用Green散度定理,得到了一个J.Simons型积分不等式,推广了已有结果.     

拟常曲率黎曼流形中具有平行平均曲率向量的子流形

研究了拟常曲率黎曼流形中具有平行平均曲率向量的紧致子流形，得到一个积分不等式。     

常曲率空间中具有平行平均曲率的完备伪脐子流形

讨论了常曲率黎曼流形中具有平行平均曲率向量场的完备伪脐子流形，得到了这类子流形为全脐子流形的一个充分条件．     

关于具有平行平均曲率向量子流形

本文研究一般黎曼流形中具有平行平均曲率向量的子流形，得到了关于这类子流形的一个积分不等式及相应的一个余维数减小的定理，推广了S．T．Yau的一个结论．     

局部对称空间中关于截面曲率的一个刚性定理

设Nn p是截面曲率K满足12<δ≤KN≤1的n p维局部对称完备黎曼流形,M是N的具有平行平均曲率向量的n维紧致子流形,我们讨论这类子流形,得到其关于截面曲率拼挤定理,将常曲率空间中的类似问题推广到局部对称空间。     

拟常曲率黎曼流形中的全脐子流形

讨论拟常曲率黎曼流形中的全脐子流形,得到关于这类子流形的两个定理.     

常曲率黎曼流形中具有平行中曲率向量的紧致伪脐子流形

研究常曲率黎曼流形N^n＋P（c）中具有平行中曲率向量的紧致伪脐子流形M^n,得到子流形M^n的内在量K,Q,σ若满足一定关系可使M^n是全脐子流形．推广了徐仙发和纪永强的有关结果．     

Sequence-directed curvature of DNA

DNAs from both prokaryotic and eukaryotic organisms have yielded restriction fragments which manifest markedly anomalous electrophoretic behaviour (reduced mobility) when run on polyacrylamide gels. We have shown previously that the abnormal electrophoretic behaviour of one such fragment is a consequence of stable curvature of the helix axis in solution. The molecules involved tend to contain oligo(dA)-oligo(dT) runs which are approximately in-phase with the helix repeat; however, the precise structural elements responsible for DNA curvature have not been identified. One popular model for curvature invokes a non-coplanar 'wedge-like' conformation of ApA/TpT dinucleotide pairs. Despite a lack of direct evidence in support of this model, it has been used to provide quantitative estimates of curvature. To critically evaluate the ApA wedge model, we have performed an electrophoretic analysis of a series of closely related DNA polymers in which oligo(dA)-oligo(dT) runs of different polarity were compared. We conclude that ApA dinucleotide wedges cannot account for DNA curvature. Therefore, quantitative estimates for ApA wedge deformations, based solely on apparent curvature, cannot be correct.     

局部对称拟常曲率黎曼流形中具有平行平均曲率向量的子流形

得到了局部对称拟常曲率黎曼流形中的拼挤常数,使得常曲率空间形式的相应拼挤常数是它的特例.     

具有标量曲率的Randers流形

文中主要研究了具有曲率的一类特殊的芬斯勒流形——Randers流形。首先回顾了芬斯勒流形的基本知识及芬斯勒流形的导航问题的有关事实。进一步通过对导航问题的研究转化为将Randers流形转化为黎曼流形的研究,利用Schur引理,证明了Randers流形具有标量旗曲率当且仅当该流形具有常曲率这一性质。     

~(n+1)(C)中具有常中曲率的Dupin超曲面

给出了 Dupin 超曲面的基本公式,由此研究了 Dupin 超曲面成为等参超曲面的条件。设 M 是(C)的具常中曲率 H 的 Dupin 超曲面,λ_1<λ_2<…<λ_g 是 M 所有不同的主曲率,如果λ_η为常数(η≥3)且 C+λ_1λ_η≥0,或者,M具有三个不同主曲率,且λ_1为常数(λ_1≠H)则 M 是等参超曲面。     

Prescribing symmetric scalar curvature onS 2

The problem of prescribing scalar curvature in S2 is discussed, and the solvability of the e-quation - Δu + 2-Reu = 0 on S2, is given, where R∈C0(S2). It is known that there are some obstructions . Some new results are given by seeking a solution of the minimax type. For example, supposing that R is G symmetric and is constant on the set of fixed points on S2 under G (where G is a subgroup of O(3)), It is proved that the equation is solvable if and only if R is positive somewhere.     

Apparent surface curvature affects lightness perception

The human visual system has the remarkable capacity to perceive accurately the lightness, or relative reflectance, of surfaces, even though much of the variation in image luminance may be caused by other scene attributes, such as shape and illumination. Most physiological, and computational models of lightness perception invoke early sensory mechanisms that act independently of, or before, the estimation of other scene attributes. In contrast to the modularity of lightness perception assumed in these models are experiments that show that supposedly 'higher-order' percepts of planar surface attributes, such as orientation, depth and transparency, can influence perceived lightness. Here we show that perceived surface curvature can also affect perceived lightness. The results of the earlier experiments indicate that perceiving luminance edges as changes in surface attributes other than reflectance can influence lightness. These results suggest that the interpretation of smooth variations in luminance can also affect lightness percepts.     

一种新型的光纤曲率传感器

开发了一种新型的埋入式光纤曲率传感器 ,以结构的曲率变形对传感器的输出光强实现强度调制 .对传感器的静态和动态特性作了分析 ,提出了该传感器的传感机理 ,对传感器的结构作了改进 .将此传感器埋入树脂基复合材料板内部 ,测量板的弯曲变形 .可利用此曲率传感器组成准分布式传感系统检测智能结构的形状变化 .     

几类特殊曲面曲线的法曲率测地曲率和测地挠率的计算

特殊曲面曲线是曲面论中的一个重要研究对象,坐标曲线、渐近曲线、曲率线和测地线是曲面上常见的几类特殊曲面曲线,而法曲率、测地曲率和测地挠率又是曲面曲线的三个重要的数字特征。本文首先推导出法曲率、测地曲率和测地挠率的性质;其次,列举了三者之间最常见的几种关系;最后,给出上述几类特殊曲面曲线的法曲率、测地曲率和测地挠率的计算公式。