共查询到20条相似文献,搜索用时 625 毫秒
1.
P. M. G. Manchón 《Acta Mathematica Hungarica》1998,81(1-2):21-40
In this paper we introduce new definitions of submanifold and immersion in the context of infinite dimensional manifolds with corners. We show that they are the natural concepts in this context by giving positive answers to the problems of transitivity of submanifolds, inverse image of submanifolds and transversality, the problem of good immersion in quadrants of Banach spaces and the relation between a map being differentiable and its graph being a submanifold. 相似文献
2.
双曲空间Hn+p(-1)中具常数量曲率的完备子流形 总被引:3,自引:0,他引:3
设Mn是Hn p(-1)中具有常标准数量曲率的n维完备子流形,本文证明了这种完备子流形的某些内蕴刚性定理和分类定理,并对超曲面的情形进行了研究. 相似文献
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4.
Finite Type Non—Minimal Submanifolds 总被引:1,自引:1,他引:0
The notion of finite type xubmanifolds was introduced by B.Y.Chen.In this paper we consider the characteristics and the classifications of finite type non-minimal submanifolds.The characteristic theorems of 2-type Chen submanifolds、mass-symmetric hypersurfaces and Dupin hypersurfaces in Es^m are obtained.The classification theorems of 3-type hypersurfaces and null 2-type curves in Es^m are also proved. 相似文献
5.
We deal with complex submanifolds in indefinite space forms. In particular, submanifolds with large index of relative nullity are emphasized. In that context, we prove cylinder theorems in terms of indefinite metrics. We also give a systematic way of constructing a family of new complete and closed indefinite complex submanifolds in the projective setting.In the appendix, we show that the method used for complex cases can be applied to real indefinite geometry. We prove real cylinder theorems including B-scrolls in the general signature. We also show two decomposition lemmas which clarify the relationships between the Hartman-Nirenberg cylinder theorem and slanted cylinder theorems in indefinite geometry. 相似文献
6.
Nilton Moura Barroso Neto Qiaoling Wang 《Journal of Mathematical Analysis and Applications》2012,389(1):694-700
We prove some Bernstein-type rigidity theorems for complete submanifolds in a Euclidean space and space-like submanifolds of a Lorentzian space. In particular, we obtain a Bernstein rigidity theorem for complete minimal submanifolds of arbitrary codimension in Euclidean space. 相似文献
7.
研究了deSitter空间中具有常数量曲率的类空子流形,利用活动标架的方法,证明了这类子流形的某些刚性定理,推广了已有的一些结果. 相似文献
8.
本文研究S~n中不含脐点、Moebius形式为零且具Moebius平坦法丛的子流形的Moebius特性。分别利用子流形的Moebius Ricci曲率与Blaschke张量、Moebius标准数量曲率以及Blaschke张量与Moebius标准数量曲率之间所满足的某种内蕴关系刻画了S~n中子流形的Moebius特性,得到了S~n中法丛平坦子流形的两个分类定理。 相似文献
9.
This paper shows that an arbitrary generic submanifold in a complex manifold can be deformed into a 1-parameter family of generic submanifolds satisfying strong nondegeneracy conditions. The proofs use a careful analysis of the jet spaces of embeddings satisfying certain nondegeneracy properties, and also make use of Thom's transversality theorem, as well as the stratification of real-algebraic sets. Optimal results on the order of nondegeneracy are given. 相似文献
10.
We study a class of submanifolds, called Generalized Cauchy-Riemann (GCR) lightlike submanifolds of indefinite Sasakian manifolds as an umbrella of invariant, screen real, contact CR lightlike subcases [8] and real hypersurfaces [9]. We prove existence and non-existence theorems and a characterization theorem on minimal GCR-lightlike submanifolds. 相似文献
11.
Barbara Opozda 《Geometriae Dedicata》1998,69(1):1-14
We propose to study n-dimensional purely real submanifolds of the standard affine complex space Cn from an affine point of view. Such submanifolds are naturally endowed with a unique transversal bundle. Fundamental theorems are given as well as a theorem of Cartan–Norden type. Examples illustrating particular affine properties of such submanifolds are provided. 相似文献
12.
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
13.
Andreas Floer 《纯数学与应用数学通讯》1988,41(6):775-813
The symplectic action can be defined on the space of smooth paths in a symplectic manifold P which join two Lagrangian submanifolds of P. To pursue a new approach to the variational theory of this function, we define on a subset of the path space the flow whose trajectories are given by the solutions of the Cauchy-Riemann equation with respect to a suitable almost complex structure on P. In particular, we prove compactness and transversality results for the set of bounded trajectories. 相似文献
14.
The Fundamental and Rigidity Theorems for Pseudohermitian Submanifolds in the Heisenberg Groups
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Hung-Lin Chiu 《数学研究》2021,54(1):1-27
In this paper, we study some basic geometric properties of pseudohermitian
submanifolds of the Heisenberg groups. In particular, we obtain the uniqueness and
existence theorems, and some rigidity theorems. 相似文献
15.
Summary We introduce a class of submanifolds, namely, Generalized Cauchy--Riemann (GCR) lightlike submanifolds of indefinite Kaehler
manifolds. We show that this new class is an umbrella of invariant (complex), screen real [8] and CR lightlike [6] submanifolds.
We study the existence (or non-existence) of this new class in an indefinite space form. Then, we prove characterization theorems
on the existence of totally umbilical, irrotational screen real, complex and CR minimal lightlike submanifolds. We also give
one example each of a non totally geodesic proper minimal GCR and CR lightlike submanifolds. 相似文献
16.
Yueshan XIONG 《Frontiers of Mathematics in China》2015,10(2):395
The homotopy connectedness theorem for invariant immersions in Sasakian manifolds with nonnegative transversal q-bisectional curvature is proved. Some Barth-Lefschetz type theorems for minimal submanifolds and (k, ?)-saddle submanifolds in Sasakian manifolds with positive transversal q-Ricci curvature are proved by using the weak (?-)asymptotic index. As a corollary, the Frankel type theorem is proved. 相似文献
17.
BOUNDARYVALUEPROBLEMSFORTHIRDORDERDIFFERENTIALEQUATIONS王金枝内蒙古大学,邮编:010021BOUNDARYVALUEPROBLEMSFORTHIRDORDERDIFFERENTIALEQUATI... 相似文献
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19.
Nobusumi Sagara 《Set-Valued and Variational Analysis》2010,18(1):1-28
This paper investigates a relationship between the maximum principle with an infinite horizon and dynamic programming and
sheds new light upon the role of the transversality condition at infinity as necessary and sufficient conditions for optimality
with or without convexity assumptions. We first derive the nonsmooth maximum principle and the adjoint inclusion for the value
function as necessary conditions for optimality. We then present sufficiency theorems that are consistent with the strengthened
maximum principle, employing the adjoint inequalities for the Hamiltonian and the value function. Synthesizing these results,
necessary and sufficient conditions for optimality are provided for the convex case. In particular, the role of the transversality
conditions at infinity is clarified. 相似文献
20.
§ 1 IntroductionLet x:M→ Sn+p be an n-dimensional submanifold in the unit sphere without umbilicpoints.Let { ei} be a local orthonormal basis with respectto the firstfundamental form I=dx·dx with dual basis{ θi} .Let II =∑ijαhαijθiθjeαbe the second fundamental form of xand H =∑αHαeαbe the mean curvature vector of x,where we use the range of indices:1≤ i,j,k,l≤ n, n + 1≤α,β,γ≤ n + p,Hα=1n∑ihαij,{ eα} is a local orthonormal basis forthe normal bundle ofx.We defi… 相似文献