Parallel and totally geodesic hypersurfaces of non-reductive homogeneous four-manifolds

We classify totally geodesic and parallel hypersurfaces of four-dimensional non-reductive homogeneous pseudo-Riemannian manifolds.     

Totally umbilic null hypersurfaces in generalized Robertson–Walker spaces

We show that there is a correspondence between totally umbilic null hypersurfaces in generalized Robertson–Walker spaces and twisted decompositions of the fibre. This allows us to prove that nullcones are the unique totally umbilic null hypersurfaces in the closed Friedmann Cosmological model. We also apply this kind of ideas to static spaces, in particular to Reissner–Nordström and Schwarzschild exterior spacetimes.     

共形空间${\mathbb Q}^{n+1}_1$中类空超曲面的拼挤问题

通过对第二共形基本形式的模长平方作拼挤,给出Clifford超柱面的一个共形特征.     

涉及复代数超曲面的全纯映射正规族

本文研究了涉及固定超曲面的全纯映照的正规性问题。利用Aladro 和Krantz对全纯映射族正规性的刻画和Shirosahi建立的一系列涉及一些特殊复代数超曲面的Picard 型定理,得到了全纯映射族的一些正规定则。     

Homogeneous hypersurfaces in complex hyperbolic spaces

We study the geometry of homogeneous hypersurfaces and their focal sets in complex hyperbolic spaces. In particular, we provide a characterization of the focal set in terms of its second fundamental form and determine the principal curvatures of the homogeneous hypersurfaces together with their multiplicities.      

Classification of hypersurfaces with constant Laguerre eigenvalues in R~n

Let x:M → Rn be an umbilical free hypersurface with non-zero principal curvatures.Then x is associated with a Laguerre metric g,a Laguerre tensor L,a Laguerre form C,and a Laguerre second fundamental form B,which are invariants of x under Laguerre transformation group.An eigenvalue of Laguerre tensor L of x is called a Laguerre eigenvalue of x.In this paper,we classify all oriented hypersurfaces with constant Laguerre eigenvalues and vanishing Laguerre form.     

基于伪类光超曲面奇点分类的教学研究

在微分几何的教学中,曲线,曲面理论是最主要的基础理论知识.欧氏空间中密切曲线在微分几何学中具有重要的研究价值.主要运用具有类光向量的费雷内标架讨论在四维Minkowski空间中与欧氏空间不同的一类特殊密切曲线(伪类光曲线)的一些几何性质,同时通过横截性原理给出了由伪类光曲线生成的伪类光超曲面的局部几何性质与奇点分类.     

Characterizations of some homogeneous Hopf real hypersurfaces in a nonflat complex space form by extrinsic shapes of trajectories

We characterize some homogeneous Hopf real hypersurfaces in a nonflat complex space form by studying trajectories for Sasakian magnetic fields whose extrinsic shapes are tangentially of order 2.