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41.
Wolfgang M. Schmidt 《Transactions of the American Mathematical Society》2007,359(5):2221-2241
Questions on rational approximations to a real number can be generalized in two directions. On the one hand, we may ask about ``approximation' to a point in by hyperplanes defined over the rationals. That is, we seek hyperplanes with small distance from the given point. On the other hand, following Wirsing, we may ask about approximation to a real number by real algebraic numbers of degree at most .
The present paper deals with a common generalization of both directions, namely with approximation to a point in by algebraic hypersurfaces, or more generally algebraic varieties defined over the rationals.
42.
43.
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.
相似文献
44.
Fei Guo 《Journal of Mathematical Analysis and Applications》2009,353(1):88-98
In this paper, the multiplicity of Lagrangian orbits on C2 smooth compact symmetric star-shaped hypersurfaces with respect to the origin in R2n is studied. These Lagrangian orbits begin from one Lagrangian subspace and end on another. An infinitely many existence result is proved via Z2-index theory. This is a multiplicity result about the Arnold Chord Conjecture in some sense, and is a generalization of the problem about the multiplicity of Lagrangian orbits beginning from and ending on the same Lagrangian subspace which was considered in the authors' previous paper [F. Guo, C. Liu, Multiplicity of Lagrangian orbits on symmetric star-shaped hypersurfaces, Nonlinear Anal. 69 (4) (2008) 1425-1436]. 相似文献
45.
The present work is divided into three parts. First we study the null hypersurfaces of the Minkowski space , classifying all rotation null hypersurfaces in . In the second part we start our analysis of the submanifold geometry of the null hypersurfaces. In the particular case of the -dimensional light cone, we characterize its totally umbilical spacelike hypersurfaces, show the existence of non-totally umbilical ones and give a uniqueness result for the minimal spacelike rotation surfaces in the -dimensional light cone. In the third and final part we consider an isolated umbilical point on a spacelike surface immersed in the 3-dimensional light cone of and obtain the differential equation of the principal configuration associated to this point, showing that every classical generic Darbouxian principal configuration appears in this context. 相似文献
46.
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
47.
Hui Liu 《数学学报(英文版)》2012,28(5):885-900
In this paper, let Σ R2n be a symmetric compact convex hypersurface which is ( r, R )- pinched with R/r (5/3)1/2 . Then Σ carries at least two elliptic symmetric closed characteristics; moreover, Σ carries at least E [ n-1/2 ] + E [ n-1/3 ] non-hyperbolic symmetric closed characteristics. 相似文献
48.
We characterize homogeneous real hypersurfaces M's of type (A
1), (A
2) and (B) of a complex projective space in the class of real hypersurfaces by studying the holomorphic distribution T
0
M of M. 相似文献
49.
Integral curves of characteristic vector fields of real hypersurfaces in nonflat complex space forms
In this paper, we study real hypersurfaces all of whose integral curves of characteristic vector fields are plane curves in
a nonflat complex space form.
相似文献
50.
本文的主要结果是:Lorentz-Minkowski空间中介于两个同心伪圆柱面之间的完备、类空、常平均曲率超曲面必为伪圆柱面,即乘积空间R~k×H~(n-k).对于常高阶平均曲率的情况,如果截曲率有下界,那么介于两个同心伪球面之间的完备类空超曲面必为伪球面. 相似文献