共查询到20条相似文献,搜索用时 31 毫秒
1.
In this note we provide a direct proof of the complete classification of conformally flat isoparametric submanifolds of Euclidean space. 相似文献
2.
RemarksontheVeroneseGeneratingSubmanifoldsinMinkoskiSpaceHuConge(胡聪娥)(HenanUniversity,Kaifeng,475001)Abstract:Inthispaper,the... 相似文献
3.
[Nie C X,Wu C X,Regular submanifolds in the conformal space Q_p~n,ChinAnn Math,2012,33B(5):695-714]中研究了共形空间Q_s~n中的正则子流形,并引入了共形空间Q_s~n中的子流形理论.本文作者将分类共形空间Q_s~n中的Blaschke拟全脐子流形,证明伪Riemann空间形式中具有常数量曲率和平行的平均曲率向量场的正则子流形是共形空间中的Blaschke拟全脐子流形;反之,共形空间中的Blaschke拟全脐子流形共形等价于伪Riemann空间形式中具有常数量曲率和平行的平均曲率向量场的正则子流形.这一结论可看作是共形空间Q_s~n中共形迷向子流形分类定理的推广. 相似文献
4.
本文给出了四元数射影空间中紧致全实伪脐子流形关于截面曲率和Ricci曲率的Pinching定理,并推广和改进了四元数射影空间中紧致全实极小流形的一些结果. 相似文献
5.
In this paper,the higher dimensional conjecture on Veronese generating subman-ifolds proposed by Prof. SUN Zhen-zu is generalized to Pseudo-Euclidean Space L1(m+1), it is proved that in the higher dimentional Lorentz Space L1(m+1), the generating submanifolds of an n dimentional submanifold of Pseudo-Riemannian unit sphere S1m is an n+1 dimentional minimal submanifold of S1(m+1) in L1(m+2) and is of 1-type in L1(m+2). 相似文献
6.
In this paper, an estimate of the constant scalar curvature of a compact non- minimal pseudo-umbilical Lagrangian submanifold in CP3 is obtained. As its application, we prove that compact Einstein pseudo-umbilical Lagrangian submanifolds in CP3 must be minimal. 相似文献
7.
In this article, we construct some spacelike austere submanifolds in pseduoEuclidean spaces. We also get some indefinite special Lagrangian submanifolds by constructing twisted normal bundle of spacelike austere submanifolds in pseduo-Euclidean spaces. 相似文献
8.
本文获得$\mathbb{C}P^3$中非极小的紧致伪脐Lagrange子流形常数数量曲率的一个估计. 作为其应用, 我们证明了$\mathbb{C}P^3$中紧致Einstein伪脐Lagrange子流形必是极小的. 相似文献
9.
证明了复射影空间中两种类型法丛平坦的全实迷向予流形必是极小的,并在紧致的情形确定了它们的具体形状. 相似文献
10.
Let Mn be a totally real pseudo-umbilical submanifold in a complex projective space CPn+p. In this paper, we study the position of completeness of Mn. By choosing a suitable frame field, we obtain a rigidity theorem such that Mn becomes totally umbilical submanifold and improve the related results. 相似文献
11.
Our first result is a reduction inequality for the displacement energy. We apply it to establish some new results relating symplectic capacities and the volume of a Lagrangian submanifold in a number of different settings. In particular, we prove that a Lagrange submanifold always bounds a holomorphic disc of area less than , where is some universal constant. We also explain how the Alexandroff-Bakelman-Pucci inequality is a special case of the above inequalities. Our inequality on displacement of reductions is also applied to yield a relation between length of billiard trajectories and volume of the domain. Two simple results concerning isoperimetric inequalities for convex domains and the closure of the symplectic group for the norm are included. 相似文献
13.
A singular foliation on a complete Riemannian manifold M is said to be Riemannian if each geodesic that is perpendicular at one point to a leaf remains perpendicular to every leaf it meets. We prove that if the distribution of normal spaces to the regular leaves is integrable, then each leaf of this normal distribution can be extended to be a complete immersed totally geodesic submanifold (called section), which meets every leaf orthogonally. In addition the set of regular points is open and dense in each section. This result generalizes a result of Boualem and solves a problem inspired by a remark of Palais and Terng and a work of Szenthe about polar actions. We also study the singular holonomy of a singular Riemannian foliation with sections (s.r.f.s. for short) and in particular the tranverse orbit of the closure of each leaf. Furthermore we prove that the closures of the leaves of a s.r.f.s on M form a partition of M which is a singular Riemannian foliation. This result proves partially a conjecture of Molino. 相似文献
14.
Let SO(n) act in the standard way on Cn and extend this action in the usual way to Cn 1 =C Cn. It is shown that a nonsingular special Lagrangian submanifold L (?) Cn 1 that is invariant under this SO(n)-action intersects the fixed C (?) Cn 1 in a nonsingular real-analytic arc A (which may be empty). If n > 2, then A has no compact component. Conversely, an embedded, noncompact nonsingular real-analytic arc A(?)C lies in an embedded nonsingular special Lagrangian submanifold that is SO(n)-invariant. The same existence result holds for compact A if n = 2. If A is connected, there exist n distinct nonsingular SO(n)-invariant special Lagrangian extensions of A such that any embedded nonsingular SO(n)-invariant special Lagrangian extension of A agrees with one of these n extensions in some open neighborhood of A. The method employed is an analysis of a singular nonlinear pde and ultimately calls on the work of Gerard and Tahara to prove the existence of the extension. 相似文献
15.
A class of minimal almost complex submanifolds of a Riemannian manifold
with a parallel quaternionic structure Q, in particular of a 4-dimensional oriented Riemannian manifold, is studied. A notion of Kähler submanifold is defined. Any Kähler submanifold is pluriminimal. In the case of a quaternionic Kähler manifold
of non zero scalar curvature, in particular, when
is an Einstein, non Ricci-flat, anti-self-dual 4-manifold, we give a twistor construction of Kähler submanifolds M2n of maximal possible dimension 2 n. More precisely, we prove that any such Kähler submanifold M2n of
is the projection of a holomorphic Legendrian submanifold
of the twistor space
of
, considered as a complex contact manifold with the natural holomorphic contact structure
. Any Legendrian submanifold of the twistor space
is defined by a generating holomorphic function. This is a natural generalization of Bryants construction of superminimal surfaces in S4= P1. Mathematics Subject Classification (1991) Primary: 53C40; Secondary: 53C55 相似文献
16.
We prove that minimal (extrinsically) homogeneous submanifolds of the Euclidean space are totally geodesic. As an application, we obtain that a complex homogeneous submanifold of C
N
must be totally geodesic. 相似文献
18.
Let S ⊂ ℂ
n
be a compact connected 2-codimensional submanifold. If n ⩾ 3, essentially local conditions and the assumption: every complex point of S is elliptic imply the existence of a projection in ℂ
n
of a Levi-flat (2 n−1)-subvariety whose boundary is S (Dolbeault, Tomassini, Zaitsev, 2005). We extend the result when S is homeomorphic to a sphere and has one hyperbolic point.
For n = 2 many results are known since the 1980’s and a new result with a very technical hypothesis is announced.
Dedicated to Professor LU QiKeng on the occasion of his 80th birthday 相似文献
19.
We show that a Lagrangian submanifold of a complex space form attaining equality in the inequality obtained by Oprea in [8],
must be totally geodesic.
相似文献
20.
Vidussi was the first to construct knotted Lagrangian tori in simply connected four-dimensional manifolds. Fintushel and Stern introduced a second way to detect such knotting. This note demonstrates that similar examples may be distinguished by the fundamental group of the exterior. 相似文献
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