共查询到20条相似文献,搜索用时 31 毫秒
2.
Kolá Martin 《中国科学A辑(英文版)》2006,49(11):1633-1641
3.
Martin Kolář 《中国科学 数学(英文版)》2006,49(11):1633-1641
4.
研究了$(n+p)$维双曲空间$\mathbb{H}^{n+p}$中完备非紧子流形的第一特征值的上界.特别地,证明了$\mathbb{H}^{n+p}$中具有平行平均曲率向量$H$和无迹第二基本形式有限$L^q(q\geq n)$范数的完备子流形的第一特征值不超过$\frac{(n-1)^2(1-|H|^2)}{4}$,和$\mathbb{H}^{n+1}(n\leq5)$中具有常平均曲率向量$H$和无迹第二基本形式有限$L^q(2(1-\sqrt{\frac{2}{n}})
相似文献
5.
A. V. Loboda 《Siberian Mathematical Journal》2001,42(6):1111-1114
We study aspherical tube hypersurfaces of the two-dimensional complex space which satisfy the local homogeneity condition. We prove that the holomorphic homogeneity of such a surface in the analytic case is equivalent to its affine homogeneity. The proof bases on the properties of the holomorphic invariants of tube hypersurfaces which are constructed by means of the Moser normal form. 相似文献
6.
Various questions of classical differential geometry lead to the problem of determining all those hypersurfaces of euclidean space for which the covariant derivative of the second fundamental form vanishes identically. In the first part of this note, we investigate these hypersurfaces; the result is summarized in the theorem of the opening paragraph, whose proof is based in the decomposition theorem of De Rham (see e.g. [6], pp. 180–186). Applying this result in the second part of the note, we give local characterizations of the Euclidean sphere. 相似文献
7.
A.-M. LI H. L. LIU A. SCHWENK-SCHELLSCHMIDT U. SIMON C. P. WANG 《Geometriae Dedicata》1997,66(2):203-221
We introduce the concept of a relative Tchebychev hypersurface which extends that of affine spheres in equiaffine geometry and also that of centroaffine Tchebychev hypersurfaces and give partial local and global classifications for this new class. Our tools concern a new operator and interesting properties of the traceless part of the cubic form. 相似文献
8.
利用奇点理论研究了广义de Sitter空间中具有Lorentzian法空间的一类超曲面.介绍了这类超曲面的局部微分几何,定义了nullcone Gauss映射及nullcone高度函数族,进而研究了nullcone高度函数族的性质及nullcone高斯映射的几何意义,最后研究了这类超曲面的通有性质. 相似文献
9.
Andreas Savas-Halilaj 《Journal of Geometric Analysis》2013,23(3):1032-1057
The aim of this paper is to complete the local classification of minimal hypersurfaces with vanishing Gauss–Kronecker curvature in a 4-dimensional space form. Moreover, we give a classification of complete minimal hypersurfaces with vanishing Gauss–Kronecker curvature and scalar curvature bounded from below. 相似文献
10.
11.
Fortuné Massamba 《Mediterranean Journal of Mathematics》2013,10(2):1079-1099
Null hypersurfaces have metrics with vanishing determinants and this degeneracy of these metrics leads to several difficulties. In this paper, null hypersurfaces of indefinite Kenmotsu space forms, tangent to the structure vector field, are studied with specific attention to locally symmetric, semi-symmetric and Ricci semi-symmetric null hypersurfaces. We show that locally symmetric and semi-symmetric null hypersurfaces are totally geodesic and parallel. These also hold for Ricci semi-symmetric null hypersurfaces, under a certain condition. We prove that, in null Einstein hypersurfaces of an indefinite Kenmotsu space form, tangent to the structure vector field, the local symmetry, semisymmetry and Ricci semi-symmetry notions are equivalent. For totally contact umbilical null hypersurfaces, we show that there are η-“Weyl” connections adapted to the induced structure on the null hypersurface. 相似文献
12.
For hypersurfaces with regular Weingarten operator in nonflat space forms we study the relations between the intrinsic geometry of the third fundamental form metric and the extrinsic geometry of the hypersurface. We prove a theorema-egregium-type result for this metric and, in particular, give a local classification of hypersurfaces in case of an Einstein structure of this metric.Partially supported by the project 19701003 of NSFC.The geometry groops at TU Berlin and KU Leuven cooperate within the GA DGET program. 相似文献
13.
Martin Kolá? 《Mathematische Annalen》2012,354(3):813-825
We consider the convergence problem for normal forms on finite type hypersurfaces in dimension two, constructed in Kolá? (Math Res Lett 12:897?C910, 2005). Two families of examples of hypersurfaces with divergent normal form are given. The results also show that the divergence phenomenon cannot be avoided by a modification of the normal form construction. 相似文献
14.
In this paper, by Nomizu’s method and some technical treatment of the asymmetry of the F-Weingarten operator, we obtain a classification of complete anisotropic isoparametric hypersurfaces, i.e., hypersurfaces
with constant anisotropic principal curvatures, in Euclidean spaces, which is a generalization of the classical case for isoparametric
hypersurfaces in Euclidean spaces. On the other hand, by an example of local anisotropic isoparametric surface constructed
by B. Palmer, we find that in general anisotropic isoparametric hypersurfaces have both local and global aspects as in the
theory of proper Dupin hypersurfaces, which differs from classical isoparametric hypersurfaces. 相似文献
15.
Huang Xuanguo 《数学年刊B辑(英文版)》1985,6(2):177-184
Let M be a 3-dimersional complete and connected hypersurface immersed in R~4. If thescalar curvature R and the mean curvature |H| of M are constants, where |H|≠0, R≥0,then there are only three cases: R=6|H|~2, 9/2|H|~2 and 0. Moreovon we can find somehypersurfaces appropriate to these cases. 相似文献
16.
We give local criteria for smooth non-embeddability of Levi-flat manifolds. For this purpose, we pose an analogue of Ueda theory on the neighborhood structure of hypersurfaces in complex manifolds with topologically trivial normal bundles. 相似文献
17.
Luis J. Alías S. Carolina García-Martínez Marco Rigoli 《Annals of Global Analysis and Geometry》2012,41(3):307-320
In this article, we establish a weak maximum principle for complete hypersurfaces with constant scalar curvature into Riemannian
space forms, and give some applications to estimate the norm of the traceless part of its second fundamental form. 相似文献
18.
In this paper, we develop the notion of screen isoparametric hypersurface for null hypersurfaces of Robertson–Walker spacetimes. Using this formalism we derive Cartan identities for the screen principal curvatures of null screen isoparametric hypersurfaces in Lorentzian space forms and provide a local characterization of such hypersurfaces. 相似文献
19.
In this paper, we first set up an alternative fundamental theory of Möbius geometry for any umbilic-free spacelike hypersurfaces in four dimensional Lorentzian space form, and prove the hypersurfaces can be determined completely by a system consisting of a function W and a tangent frame {Ei}. Then we give a complete classification for spacelike Möbius homogeneous hypersurfaces in four dimensional Lorentzian space form. They are either Möbius equivalent to spacelike Dupin hypersurfaces or to some cylinders constructed from logarithmic curves and hyperbolic logarithmic spirals. Some of them have parallel para-Blaschke tensors with non-vanishing Möbius form. 相似文献
20.
A. V. Loboda 《Mathematical Notes》1996,59(2):148-157