Lorentz-Minkowski空间中旋转W超曲面

1841年,D elaunay获得如下定理:如果在一平面上沿定直线滚动一条二次圆锥直线,然后将其焦点的轨迹绕定直线旋转,则所得到的曲面具有常数平均曲率,反之,所有旋转常数平均曲率曲面(除球面外)都有如此构造.本文将以上的D elaunay定理推广到Lorentz-M inkow sk i空间Rn1 1中类空的Sm型旋转W超曲面.     

SUBMANIFOLDS OF PRODUCT RIEMANNIAN MANIFOLD

1IntroductionLetUandVbeRiemannianmanffolds,withthedimensionn1andn2respectively.UxVistheRiemannianproductofUandV.WedenotebyPandQtheprojectionmappingsofT(UxV)toTUaildTVrespectively.ThenwehaveWeputJ=P-Q.ItiseasytoseethatJ~=I.WedefineaRiemannianmetricofUxVbyg(X,Y)==g1(PX,PY) g2(QX,QY),wllereg1andg2areRiemannia11metricofUandVrespectively.ItfollowsthatBy7wedellotetheg'sLevi-Civitaconnection.ThenwecaneasilyseethatInfact,Frollltlledefillitiollofg,wecangetthatUalldVareallgeodesicsub…     

Ricci曲率平行的一类Riemann流形的C~∞紧性(英文)

本文证明,在Ｇｒｏｍｏｖ－Ｈａｕｓｄｏｒｆｆ拓扑下,Ｒｉｃｃｉ曲率平行,截面曲率和单一半径有下界,体积有上界的Ｒｉｅｍａｎｎ流形的集合是ｃ∞紧的．作为应用,我们证明一个ｐｉｎｃｈｉｎｇ结果,即在某些条件下,Ｒｕｃｃｉ平坦的流形必定平坦．     

Lorentz-Minkowski空间中给定主曲率函数的旋转超曲面

给出(n,1)型orentz-Minkowski空间中给定主曲率函数的旋转类空超曲面的位置向量场,通过计算超曲面的主曲率,证明了这类超曲面的存在性.     

局部对称黎曼流形中的极小子流形

In this paper, we discuss the compact minimal submanifolds in locally symmetric Riemannian manifolds. Two Pinching theorems are obtained and two corresponding results of Chern, S. S. and Yau S. T. are generalized.     

Remarks on Complete Spacelike Hyper-surfaces with Constant Mean Curvature in the de Sitter Space

Let M be an n(≥3)-dimensional completely non-compact spacelike hypersurface in the de Sitter space S1 (n+1) (1) with constant mean curvature and non negative sectional curvature. It is proved that M is isometric to a hyperbolic cylinder or an Euclidean space if H ≥1. When 2(n-1)~(1.2)/n < H < 1, there exists a complete rotation hypersurfaces which is not a hyperbolic cylinder.     

Minkowski空间中带超平面边界的紧致类空超曲面

In this paper, we study the relations between a compact spacelike hypersurface with hy-perplanar boundary in the (n 1)- dimensional Minkowski space-time L^n 1 being totally umbilicaland its hyperplanar boundary in a fixed hyperplane π of L^(n 1) being totally umbilical under certainconditions. We give the sufficient conditions for such hypersurface and its hyperplanar boundary tobe totally umbilical in their respective ambients.     

球面上紧致子流形的等谱问题

本文讨论球面上伪脐子流形与全脐子流形的等谱问题．     

向量场的Nielsen数

对于紧致流形M上的任意一个向量场X，定义了一个由向量场X确定的自映射fX：M→M，使得向量场X的奇异点均为fX的不动点．证明了向量场的Nielsen数是不依赖于向量场选取的量．