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聂昌雄 《数学年刊A辑(中文版)》2015,36(1):59-68
[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
3.
《数学年刊A辑(中文版)》2015,(1)
[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.
该文证明了复射影空间中两种类型的法丛平坦全实伪脐子流形必是极小的,并在紧致的情形确定了它们的具体形状.此外,还说明了复射影空间中的全实全脐子流形一定不是法丛平坦的. 相似文献
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研究近拟常曲率黎曼流形中的紧致伪脐子流形,利用活动标架法,得到了这类子流形的Simons型积分不等式及其刚性定理. 相似文献
6.
常曲率空间中具平行平均曲率向量的子流形 总被引:6,自引:0,他引:6
本文利用第二基本形式的长度平方和平均曲率的关系研究常曲率空间中具平行平均曲率向量的子流形为全脐的pinching问题,获得了一定条件下的最佳pinching区间,并确定了phincning区间端点处对应非全脐子流形的分类. 相似文献
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本文在作者前文工作的基础上继续考查~C循环空间子流形的全脐子流形特征.给出了一个充分必要条件即定理1.从而结合已有文献我们推广并改进了Olszak文中的相应结果. 相似文献
10.
本在作前工作的基础上继续考查C∧~循环空间子流形的全脐子流形特征,给出了一个充分必要条件即定理1。从而结合已有献我们推广并改进了Olszak中的相应结果。 相似文献
11.
Jana Jurečková Pranab Kumar Sen 《Annals of the Institute of Statistical Mathematics》1990,42(2):345-357
For a general (real) parameter, let M
nbe the M-estimator and M
n
(1) be its one-step version (based on a suitable initial estimator M
n
(0)). It is known that, under certain regularity conditions, n(M
n
(1)-M
n)=O
p(1). The asymptotic distribution of n(M
n
(1)-M
n) is studied; it is typically non-normal and it reveals the role of the initial estimator M
n
(0).Work of this author was partially supported by the Office of Naval Research, Contract No. N00014-83-K-0387 相似文献
12.
《Quaestiones Mathematicae》2013,36(3-4):321-334
Abstract The group ?(Mm(A) v Mn(π)) of homotopy self-equivalence classes of two Moore spaces is faithfully represented onto a (multiplicative) group of matrices for n≥m≥3. We consider, in this note, related representations of ?(Mm(Λ)vMn(π)), for finitely generated Λ and π in the case where n≥4, and also where n=3 if ext(Λ, π)=0. The representation onto a matrix group, similar to that in the case above, is not, in general, valid. We show however that ?(M2(Λ)vMn(π)) is represented onto ?(M2(Λ))× ?(Mn(π) in this case, and that this representation determines an isomorphism with an iterated semi-direct product ?(M2(Λ)v Mn(π)) ? {(Mn(π), M2(Λ))? ext(π Λ ? π)} ? (?(M2(Λ)) × ? (Mn(π)). More generally we review, and-extend, the theory of the representation of the (generalized) near ring (XvY,XvY) onto the matrix (generalized) near-ring (XvY, XxY) where appropriate, in the case where X and Y are h-coloops; and we deduce results for the representation of ?(XvY, XvY). Some of the results published previously in the case of simply-connected CW co-h-spaces, extend to the case where X and Y are path-connected h-coloops one of which is well-pointed. We note the obstructions to the existence of a homomorphic section, and consider a number of special cases which occur when some of the groups are trivial. 相似文献
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An analogous Bonnet-Myers theorem is obtained for a complete and positively curved n-dimensional (n≥3) Riemannian manifold M
n
. We prove that if n≥4 and the curvature operator of M
n
is pointwise pinched, or if n=3 and the Ricci curvature of M
3 is pointwise pinched, then M
n
is compact.
Oblatum 4-II-1999 & 10-XI-1999?Published online: 21 February 2000 相似文献
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Beverly Brechner 《Topology and its Applications》1980,11(3):231-242
A homeomorphism of Rn onto itself is called positively regular (or EC+) iff its family of non-negative iterates is pointwise equicontinuous. For EC+ homeomorphism of Rn such that some point of Rn has bounded positive semi-orbit, the nucleus M is defined, and the following theorems are proved.Theorem 1. If such a homeomorphism h:Rn→Rn has compact nucleus M, then M is a fully invariant compact AR. Further, for n≠4,5,h:Rn/M→Rn/M is conjugate to a contraction on Rn.Theorem 2. In Rn,n≠4,5,M compact iff there existsa disk D such that h(D)?IntD.Theorem 3. In R2, either M is a disk and h|M is a rotation, or h|M is periodic. The relationship between M and the irregular set of ? is also studied. 相似文献
15.
Qintao Deng 《Archiv der Mathematik》2008,90(4):360-373
In this paper, we consider complete hypersurfaces in R
n+1 with constant mean curvature H and prove that M
n
is a hyperplane if the L
2 norm curvature of M
n
satisfies some growth condition and M
n
is stable. It is an improvement of a theorem proved by H. Alencar and M. do Carmo in 1994. In addition, we obtain that M
n
is a hyperplane (or a round sphere) under the condition that M
n
is strongly stable (or weakly stable) and has some finite L
p
norm curvature.
Received: 14 July 2007 相似文献
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A. V. Isaev 《Journal of Geometric Analysis》2008,18(3):795-799
We prove a characterization theorem for the unit polydisc Δ
n
⊂ℂ
n
in the spirit of a recent result due to Kodama and Shimizu. We show that if M is a connected n-dimensional complex manifold such that (i) the group Aut (M) of holomorphic automorphisms of M acts on M with compact isotropy subgroups, and (ii) Aut (M) and Aut (Δ
n
) are isomorphic as topological groups equipped with the compact-open topology, then M is holomorphically equivalent to Δ
n
.
相似文献
17.
A. A. Dudkin 《Journal of Mathematical Sciences》1994,69(1):851-853
For a submanifoldM
n of a Riemannian manifoldM
q, the concept of a torsion bivector at the point x M
n for given one- and two-dimensional directions fromT
x
M
n is introduced using only the first and second fundamental forms ofM
n. Its relation to the concept of Gaussian torsion is then established. It is proved that: 1) equality to zero of the torsion bivector is necessary and, whenM
n is a nondevelopable surface of a space of constant curvature with nonzero second fundamental form, is also sufficient for the "flattening" ofM
n into some totally geodesicM
n+1 inM
q; 2) when n = 2, the independence of the nonzero torsion bivector of direction characterizes a minimalM
2 inM
q.Translated from Ukrainskii Geometricheskii Sbornik, No. 34, pp. 39–42, 1991. 相似文献
18.
Complete space-like hypersurfaces with constant scalar curvature 总被引:6,自引:0,他引:6
Ximin Liu 《manuscripta mathematica》2001,105(3):367-377
Let M
n
be a complete space-like hypersurface with constant normalized scalar curvature R in the de Sitter space S
n
+
1
1 and denote . We prove that if the norm square of the second fundamental form of M
n
satisfies , then either and M
n
is a totally umbilical hypersurface; or , and, up to rigid motion, M
n
is a hyperbolic cylinder .
Received: 8 February 2001 / Revised version: 27 April 2001 相似文献
19.
F.S. Cater 《Linear algebra and its applications》1978,19(3):251-274
An n by n matrix M over a (commutative) field F is said to be central if M ? I has rank 1. We say that M is an involution if M2=I; if M is also central we call M a simple involution. We will prove that any n-by-n matrix M satisfying detM=±1 is the product of n+2 or fewer simple involutions. This can be reduced to n+1 if F contains no roots of the equation xn=(?1)n other than ±1. Any ordered field is of this kind. Our main result is that if M is any n-by-n nonsingular nonscalar matrix and if xi ∈ F such that x1?xn=detM, then there exist central matrices Mi such that M=M1?Mn and xi=detMi for i=1,…,n. We will apply this result to the projective group PGL(n,F) and to the little projective group PSL(n,F). 相似文献
20.
Regina Rotman 《Mathematische Zeitschrift》2007,257(2):427-437
Let M
n
be a closed 2-connected Riemannian manifold, such that π3(M
n
) ≠ { 0 }. In this paper we prove that either there exists a periodic geodesic on M
n
of length ≤ 6d, where d is the diameter of M
n
, or at each point p ∈ M
n
there exists a geodesic loop of length ≤ 2d. 相似文献