共查询到20条相似文献,搜索用时 0 毫秒
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Ildefonso Castro 《Geometriae Dedicata》1998,70(2):197-208
For a Lagrangian submanifold of Cn with scalar curvature and mean curvature vector H, the inequality ( n2(n-1)/n+2 |H|2) holds, and the equality is given only in open sets of the Lagrangian subspaces of n or of the Whitney sphere (cf. [RU] and also [BCM]). In this paper, a one-parameter family of Lagrangian spheres including the Whitney sphere is constructed. They satisfy a geometric equality of type = |H|2, with >0, and they are globally characterized inside the family of compact Lagrangian submanifolds with null first Betti number in Cn. 相似文献
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Sharief Deshmukh 《Comptes Rendus Mathematique》2013,351(15-16):631-634
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Sharief Deshmukh 《Comptes Rendus Mathematique》2012,350(21-22):971-974
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MatijaCENCELJ DusanREPOVS 《数学学报(英文版)》2005,21(2):435-438
Using the relation between the set of embeddings of tori into Euclidean spaces modulo ambient isotopies and the homotopy groups of Stiefel manifolds, we prove new results on embeddings of tori into Euclidean spaces. 相似文献
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We introduce a method to reduce the study of the topology of a simplicial complex to that of a simpler one. Applying this
method to complexes arising from graphs, we give topological meaning to classical graph invariants. As a consequence, we answer
some questions raised in (Ehrenborg and Hetyei in Eur. J. Comb. 27(6):906–923, 2006) on the independence complex and the dominance complex of a forest and obtain improved algorithms to compute their homotopy
types. 相似文献
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James H. Schmerl 《Discrete and Computational Geometry》2007,38(1):155-167
Suppose n ≥ 2 and
are such that X is infinite and Y is the set of vertices of an n-simplex. Then there is blue/red coloring of
such that no set similar to X is monochromatically blue and no set similar to Y is monochromatically red. 相似文献
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Dmitry N. Kozlov 《Journal of Algebraic Combinatorics》2001,14(1):27-48
The goal of this paper is twofold. First, we give an elementary introduction to the usage of spectral sequences in the combinatorial setting. Second we list a number of applications.In the first group of applications the simplicial complex is the nerve of a poset; we consider general posets and lattices, as well as partition-type posets. Our last application is of a different nature: the
-quotient of the complex of directed forests is a simplicial complex whose cell structure is defined combinatorially. 相似文献
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Enrico Leuzinger 《Geometriae Dedicata》2003,102(1):109-125
Let
be the affine Bruhat-Tits (or Euclidean) building associated to a semisimple, simply connected linear algebraic group defined over a non-Archimedean local field. We prove that there exist locally finite trees of degree 3 which are bi-Lipschitz embedded in
. As a consequence such a Euclidean building cannot be bi-Lipschitz embedded into a Hilbert space. 相似文献
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We develop an iterated homology theory for simplicial complexes. Thistheory is a variation on one due to Kalai. For a simplicial complex of dimension d – 1, and each r = 0, ...,d, we define rth iterated homology groups of . When r = 0, this corresponds to ordinary homology. If is a cone over , then when r = 1, we get the homology of . If a simplicial complex is (nonpure) shellable, then its iterated Betti numbers give the restriction numbers, h
k,j
, of the shelling. Iterated Betti numbers are preserved by algebraic shifting, and may be interpreted combinatorially in terms of the algebraically shifted complex in several ways. In addition, the depth of a simplicial complex can be characterized in terms of its iterated Betti numbers. 相似文献
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We generalize the theory of critical groups from graphs to simplicial complexes. Specifically, given a simplicial complex, we define a family of abelian groups in terms of combinatorial Laplacian operators, generalizing the construction of the critical group of a graph. We show how to realize these critical groups explicitly as cokernels of reduced Laplacians, and prove that they are finite, with orders given by weighted enumerators of simplicial spanning trees. We describe how the critical groups of a complex represent flow along its faces, and sketch another potential interpretation as analogues of Chow groups. 相似文献
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Zu Huan YU Qing Zhong LI 《数学学报(英文版)》2007,23(11):2079-2086
In this note, a construction of minimal surfaces in Euclidean 3-space is given. By using the product of Weierstrass data of two known minimal surfaces, one gets a new Weierstrass data and a corresponding minimal surface from the Weierstrass representation. 相似文献
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M. Gorbulsky 《Journal of Mathematical Sciences》2004,121(3):2326-2329
The present paper is devoted to the study of equivariant embeddings of the n-dimensional space into a Hilbert space. We consider a representation of a group of similarities. The existence of a cocycle for this representation implies the existence of an isometric embedding of a metric group into the Hilbert space. Then we describe all cocycles of a representation of the additive group of real numbers and construct an embedding of the n-dimensional space with metric d(x,y)=|x-y| into the Hilbert space. Bibliography: 5 titles. 相似文献
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We try to understand the behavior of algebraic shifting with respect to some basic constructions on simplicial complexes,
such as union, coning, and (more generally) join. In particular, for the disjoint union of simplicial complexes we prove Δ(K ˙∪ L) = Δ(Δ(K) ˙∪ Δ(L)) (conjectured by Kalai [6]), and for the join we give an example of simplicial complexes K and L for which Δ(K*L)≠Δ(Δ(K)*Δ(L)) (disproving a conjecture by Kalai [6]), where Δ denotes the (exterior) algebraic shifting operator. We develop a ‘homological’
point of view on algebraic shifting which is used throughout this work. 相似文献
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Benedek Skublics 《Order》2013,30(3):797-806
A lattice is said to be finite height generated if it is complete and every element is the join of some elements of finite height. Extending former results by Grätzer and Kiss (Order 2:351–365, 1986) on finite lattices, we prove that every finite height generated algebraic lattice that has a pseudorank function is isometrically embeddable into a geometric lattice. 相似文献
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A martingale characterization of Brownian motion on a submanifoldof Euclidean space is proved and the implications of the consequentmartingale representation are discussed. 相似文献
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For a square-free monomial ideal I ? S = k[x 1, x 2,…, x n ], we introduce the notion of quasi-linear quotients. By using the quasi-linear quotients, we give a new algebraic criterion for the shellability of a pure simplicial complex Δ over [n]. Also, we provide a new criterion for the Cohen–Macaulayness of the face ring of a pure simplicial complex Δ. Moreover, we show that the face ring of the spanning simplicial complex (defined in [2]) of an r-cyclic graph is Cohen–Macaulay. 相似文献