共查询到20条相似文献,搜索用时 281 毫秒
1.
利用欧氏空间子流形上的Bochner公式,结合极小子流形上存在的L2-Sobolev不等式,将Ni Lei的具有上界"total scalar curvature"的极小超曲面的刚性定理的结果推广到极小子流形的情形,并得到了关于极小子流形的一个曲率估计. 相似文献
2.
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
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5.
本文证明了下述结论:欧氏空间中完备连通且具有常典则支撑函数的子流形必为球面子流形或通过原点的线性子空间,从而改进了关于欧氏空间子流形的一个经典结果。 相似文献
6.
局部对称Bochner-Kaehler流形及其Kaehler子流形 总被引:3,自引:0,他引:3
本文给出局部对称的Bochner-Kaehler流形的Riemann结构以及它的Kaehler子流形为全测地子流形的几个Pinching条件,推广了关于复射影空间的Kaehler子流形的相应定理。 相似文献
7.
8.
复射影空间中极小子流形的几个整体pinching定理 总被引:4,自引:0,他引:4
王红 《数学年刊A辑(中文版)》1991,(3)
本文利用对复射影空间中紧致极小子流形的第二基本形式长度平方进行积分形式的估计方法,证明了复射影空间中紧致复子流形和紧致全实极小子流形的几个整体pinching定理。 相似文献
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本文研究球空间中子流形的共形高斯映射,用Moebius不变量刻划了该映射 为调和映射的条件.作为特例,指出球空间的2维子流形的共形高斯映射是调和映射 当且仅当该子流形是Willmore子流形. 相似文献
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Summary In [6] we introduced and investigated the notions of fI -sets and fI -continuous functions in ideal topological spaces. In this paper, we investigate their further important properties. 相似文献
14.
Jinjin Li 《Czechoslovak Mathematical Journal》2005,55(4):941-945
In this note we study the relation between k
R
-spaces and k-spaces and prove that a k
R
-space with a σ-hereditarily closure-preserving k-network consisting of compact subsets is a k-space, and that a k
R
-space with a point-countable k-network consisting of compact subsets need not be a k-space.
This work was supported by the NSF of China (10271056). 相似文献
15.
On <Emphasis Type="Italic">l</Emphasis><Subscript>2,<Emphasis Type="Italic">p</Emphasis></Subscript>-circle numbers 总被引:1,自引:1,他引:0
W.-D. Richter 《Lithuanian Mathematical Journal》2008,48(2):228-234
Circle numbers are defined to reflect the Euclidean area-content and, for p ≠ 2, suitably defined non-Euclidean circumference properties of the l
2,p
-circles, p ∈ [1, ∞]. The resulting function is continuous, increasing, and takes all values from [2, 4].
The actually chosen dual l
2,p
-geometry for measuring the arc-length is closely connected with a generalization of the method of indivisibles of Cavalieri
and Torricelli in the sense that integrating such arc-lengths means measuring area content. Moreover, this approach enables
one to look in a new way into the co-area formula of measure theory which says that integrating Euclidean arc-lengths does
not yield area content except for p = 2.
The new circle numbers play a natural role, e.g., as norming constants in geometric measure representation formulae for p-generalized uniform probability distributions on l
2,p
-circles. 相似文献
16.
ChangJian Zhao 《中国科学A辑(英文版)》2008,51(12):2172-2188
In this paper the author first introduce a new concept of L
p
-dual mixed volumes of star bodies which extends the classical dual mixed volumes. Moreover, we extend the notions of L
p
intersection body to L
p
-mixed intersection body. Inequalities for L
p
-dual mixed volumes of L
p
-mixed intersection bodies are established and the results established here provide new estimates for these type of inequalities.
This work was supported by the Natural Science Foundation of Zhejiang Province of China (Grant No. Y605065) and the Foundation
of the Education Department of Zhejiang Province of China (Grant No. 20050392) 相似文献
17.
Using elementary graded automorphisms of polytopal algebras (essentially the coordinate rings of projective toric varieties)
polyhedral versions of the group of elementary matrices and the Steinberg and Milnor groups are defined. They coincide with
the usual K-theoretic groups in the special case when the polytope is a unit simplex and can be thought of as compact/polytopal substitutes
for the tame automorphism groups of polynomial algebras. Relative to the classical case, many new aspects have to be taken
into account. We describe these groups explicitly when the underlying polytope is 2-dimensional. Already this low-dimensional
case provides interesting classes of groups.
Received: 13 December 2001 / Revised version: 24 June 2002
The second author was supported by the Deutsche Forschungsgemeinschaft, INTAS grant 99-00817 and TMR grant ERB FMRX CT-97-0107
Mathematics Subject Classification (2000): 14L27, 14M25, 19C09, 52B20 相似文献
18.
J.C. FERRANDO S. MOLL 《数学学报(英文版)》2007,23(9):1593-1600
In this paper, we show, among other results, that if X is a [separable] locally compact space X [satisfying the first countability axiom] then the space Cc (X) has countable tightness [if and only if it has bounding tightness] if and only if it is Frechet-Urysohn, if and only if Cc (X) contains a dense (LM) subspace and if and only if X is a-compact. 相似文献
19.
Ling-yun Gao 《应用数学学报(英文版)》2008,24(2):211-220
Using value distribution theory and techniques in several complex variables,we investigate the problem of existence of m components-admissible solutions of a class of systems of higher-order partial differential equations in several complex variables and estimate the number of admissible components of solutions.Some related results will also be obtained. 相似文献
20.
R. M. Mnatsakanov N. Misra Sh. Li E. J. Harner 《Mathematical Methods of Statistics》2008,17(3):261-277
For estimating the entropy of an absolutely continuous multivariate distribution, we propose nonparametric estimators based
on the Euclidean distances between the n sample points and their k
n
-nearest neighbors, where {k
n
: n = 1, 2, …} is a sequence of positive integers varying with n. The proposed estimators are shown to be asymptotically unbiased and consistent.
相似文献