共查询到20条相似文献,搜索用时 15 毫秒
1.
We give a procedure to ‘average’ canonically C1-close Legendrian submanifolds of contact manifolds. As a corollary we obtain that, whenever a compact group action leaves
a Legendrian submanifold almost invariant, there is an invariant Legendrian submanifold nearby.
Mathematics Subject Classification (2000): 53D10. 相似文献
2.
An n-dimensional submanifold X of a projective space P
N
(C) is called tangentially degenerate if the rank of its Gauss mapping gamma;; X G(n, N) satisfies 0 < rank < n. The authors systematically study the geometry of tangentially degenerate submanifolds of a projective space P
N
(C). By means of the focal images, three basic types of submanifolds are discovered: cones, tangentially degenerate hypersurfaces, and torsal submanifolds. Moreover, for tangentially degenerate submanifolds, a structural theorem is proven. By this theorem, tangentially degenerate submanifolds that do not belong to one of the basic types are foliated into submanifolds of basic types. In the proof the authors introduce irreducible, reducible, and completely reducible tangentially degenerate submanifolds. It is found that cones and tangentially degenerate hypersurfaces are irreducible, and torsal submanifolds are completely reducible while all other tangentially degenerate submanifolds not belonging to basic types are reducible. 相似文献
3.
For a germ of a smooth map f from
\mathbb Kn{{\mathbb K}^n} to
\mathbb Kp{{\mathbb K}^p} and a subgroup GWq{{{G}_{\Omega _q}}} of any of the Mather groups G for which the source or target diffeomorphisms preserve some given volume form Ω
q
in
\mathbb Kq{{\mathbb K}^q} (q = n or p) we study the GWq{{{G}_{\Omega _q}}} -moduli space of f that parameterizes the GWq{{{G}_{\Omega _q}}} -orbits inside the G-orbit of f. We find, for example, that this moduli space vanishes for GWq = AWp{{{G}_{\Omega _q}} ={{\mathcal A}_{\Omega _p}}} and A{{\mathcal A}}-stable maps f and for GWq = KWn{{{G}_{\Omega _q}} ={{\mathcal K}_{\Omega _n}}} and K{{\mathcal K}}-simple maps f. On the other hand, there are A{{\mathcal A}}-stable maps f with infinite-dimensional AWn{{{\mathcal A}_{\Omega _n}}} -moduli space. 相似文献
4.
Dominic D. Joyce 《Annals of Global Analysis and Geometry》2001,20(4):345-403
This is the third in a series of papers constructing explicit examples of special Lagrangian submanifolds in C
m
. The previous paper (Math. Ann.
320 (2001), 757–797), defined the idea of evolution data, which includes an (m – 1)-submanifold P in R
n
, and constructed a family of special Lagrangian m-folds N in C
m
, which are swept out by the image of P under a 1-parameter family of affine maps
t
: R
n
C
m
, satisfying a first-order o.d.e. in t. In this paper we use the same idea to construct special Lagrangian 3-folds in C3. We find a one-to-one correspondence between sets of evolution data with m = 3 and homogeneous symplectic 2-manifolds P. This enables us to write down several interesting sets of evolution data, and so to construct corresponding families of special Lagrangian 3-folds in C3.Our main results are a number of new families of special Lagrangian 3-foldsin C3, which we write very explicitly in parametric form. Generically these are nonsingular as immersed 3-submanifolds, and diffeomorphic to R3 or
1× R2. Some of the 3-folds are singular, and we describe their singularities, which we believe are of a new kind.We hope these 3-folds will be helpful in understanding singularities ofcompact special Lagrangian 3-folds in Calabi–Yau 3-folds. This will beimportant in resolving the SYZ conjecture in Mirror Symmetry. 相似文献
5.
In this paper, we give some characterizations for spacelike helices in Minkowski space–time E14{E_1^4}. We find the differential equations characterizing the spacelike helices and also give the integral characterizations for
these curves in Minkowski space–time E14{E_1^4}. 相似文献
6.
A complete Boolean algebra
\mathbbB{\mathbb{B}}satisfies property ((h/2p)){(\hbar)}iff each sequence x in
\mathbbB{\mathbb{B}}has a subsequence y such that the equality lim sup z
n
= lim sup y
n
holds for each subsequence z of y. This property, providing an explicit definition of the a posteriori convergence in complete Boolean algebras with the sequential
topology and a characterization of sequential compactness of such spaces, is closely related to the cellularity of Boolean
algebras. Here we determine the position of property ((h/2p)){(\hbar)}with respect to the hierarchy of conditions of the form κ-cc. So, answering a question from Kurilić and Pavlović (Ann Pure Appl Logic 148(1–3):49–62, 2007), we show that ${``\mathfrak{h}{\rm -cc}\Rightarrow (\hbar)"}${``\mathfrak{h}{\rm -cc}\Rightarrow (\hbar)"}is not a theorem of ZFC and that there is no cardinal
\mathfrakk{\mathfrak{k}}, definable in ZFC, such that ${``\mathfrak{k} {\rm -cc} \Leftrightarrow (\hbar)"}${``\mathfrak{k} {\rm -cc} \Leftrightarrow (\hbar)"}is a theorem of ZFC. Also, we show that the set { k: each k-cc c.B.a. has ((h/2p) ) }{\{ \kappa : {\rm each}\, \kappa{\rm -cc\, c.B.a.\, has}\, (\hbar ) \}}is equal to
[0, \mathfrakh){[0, \mathfrak{h})}or
[0, \mathfrak h]{[0, {\mathfrak h}]}and that both values are consistent, which, with the known equality
{k: each c.B.a. having ((h/2p) ) has the k-cc } = [\mathfrak s, ¥){{\{\kappa : {\rm each\, c.B.a.\, having }\, (\hbar )\, {\rm has\, the}\, \kappa {\rm -cc } \} =[{\mathfrak s}, \infty )}}completes the picture. 相似文献
7.
Silke Lekaus 《manuscripta mathematica》2009,130(4):495-522
We construct Laumon-1-motives Pic+a(X), Alb-a(X), Pic-a(X){{\rm Pic}^+_a(X), {\rm Alb}^-_a(X), {\rm Pic}^-_a(X)}, and Alb+a(X){{\rm Alb}^+_a(X)} associated to an algebraic variety X with complete singular locus, whose associated étale (Deligne-)1-motives coincide with Picard and Albanese motives constructed
by Barbieri Viale and Srinivas. 相似文献
8.
Georg Schneider 《Czechoslovak Mathematical Journal》2005,55(4):947-956
We consider the solution operator S: ℱμ,(p,q) → L
2(μ)(p, q) to the
-operator restricted to forms with coefficients in ℱμ = {f: f is entire and ∫ℂn
|f(z)|2 dμ(z) < ∞}. Here ℱμ,(p,q) denotes (p,q)-forms with coefficients in ℱμ, L
2(μ) is the corresponding L
2-space and μ is a suitable rotation-invariant absolutely continuous finite measure. We will develop a general solution formula
S to
. This solution operator will have the property Sv ⊥ ℱ(p,q) ∀v ∈ ℱ(p,q+1). As an application of the solution formula we will be able to characterize compactness of the solution operator in terms
of compactness of commutators of Toeplitz-operators
: ℱμ → L
2(μ). 相似文献
9.
Using the method of moving frames, we prove that any irreducible Dupin hypersurface in S
5 with four distinct principal curvatures and constant Lie curvature is equivalent by Lie sphere transformation to an isoparametric hypersurface in S
5. 相似文献
10.
Non-Existence of Stable Currents in Hypersurfaces 总被引:1,自引:0,他引:1
Xue-Shan Zhang 《Southeast Asian Bulletin of Mathematics》2000,24(1):147-154
Let Mm be a compact hypersurface in the Euclidean space Em+1. In this paper, we study the non-existence of stable integral currents in Mm and its immersed submanifolds. Some vanishing theorems concerning the homology groups of these manifolds are established.AMS Subject Classification (1991): 49Q15 53C40 53C20 相似文献
11.
A. Arkhipova 《Journal of Mathematical Sciences》2011,176(6):732-758
We prove the existence of a global heat flow u : Ω ×
\mathbbR+ ? \mathbbRN {\mathbb{R}^{+}} \to {\mathbb{R}^{N}}, N > 1, satisfying a Signorini type boundary condition u(∂Ω ×
\mathbbR+ {\mathbb{R}^{+}}) ⊂
\mathbbRn {\mathbb{R}^{n}}),
n \geqslant 2 n \geqslant 2 , and
\mathbbRN {\mathbb{R}^{N}}) with boundary ∂
[`(W)] \bar{\Omega } such that φ(∂Ω) ⊂
\mathbbRN {\mathbb{R}^{N}} is given by a smooth noncompact hypersurface S. Bibliography: 30 titles. 相似文献
12.
Michael Wemyss 《Mathematische Annalen》2011,350(3):631-659
In this paper we show that for any affine complete rational surface singularity the quiver of the reconstruction algebra can
be determined combinatorially from the dual graph of the minimal resolution. As a consequence the derived category of the
minimal resolution is equivalent to the derived category of an algebra whose quiver is determined by the dual graph. Also,
for any finite subgroup G of
GL(2,\mathbbC){{\rm GL}(2,\mathbb{C})}, it means that the endomorphism ring of the special CM
\mathbbC{\mathbb{C}} [[x, y]]
G
-modules can be used to build the dual graph of the minimal resolution of
\mathbbC2/G{\mathbb{C}^{2}/G}, extending McKay’s observation (McKay, Proc Symp Pure Math, 37:183–186, 1980) for finite subgroups of
SL(2,\mathbbC){{\rm SL}(2,\mathbb{C})} to all finite subgroups of
GL(2,\mathbbC){{\rm GL}(2,\mathbb{C})}. 相似文献
13.
Let E,F be two Banach spaces,B(E,F),B+(E,F),Φ(E,F),SΦ(E,F) and R(E,F) be bounded linear,double splitting,Fredholm,semi-Frdholm and finite rank operators from E into F,respectively. Let Σ be any one of the following sets:{T ∈Φ(E,F):Index T=constant and dim N(T)=constant},{T ∈ SΦ(E,F):either dim N(T)=constant< ∞ or codim R(T)=constant< ∞} and {T ∈ R(E,F):Rank T=constant< ∞}. Then it is known that Σ is a smooth submanifold of B(E,F) with the tangent space TAΣ={B ∈ B(E,F):BN(A)-R(A) } for any A ∈Σ. However,for ... 相似文献
14.
Lin-Feng Wang 《Annals of Global Analysis and Geometry》2010,37(4):393-402
Let M be an n-dimensional complete non-compact Riemannian manifold, dμ = e
h
(x)dV(x) be the weighted measure and
\trianglem{\triangle_{\mu}} be the weighted Laplacian. In this article, we prove that when the m-dimensional Bakry–émery curvature is bounded from below by Ric
m
≥ −(m − 1)K, K ≥ 0, then the bottom of the Lm2{{\rm L}_{\mu}^2} spectrum λ1(M) is bounded by
l1(M) £ \frac(m-1)2K4,\lambda_1(M) \le \frac{(m-1)^2K}{4}, 相似文献
15.
In this paper we use a new equivalent condition of Hamiltonian stationary Lagrangian surfaces in ℂP2 to show that any Hamiltonian stationary Lagrangian torus in ℂP2 can be constructed from a pair of commuting Hamiltonian ODEs on a finite dimensional subspace of a certain loop Lie algebra,
i.e., is of finite type.
Mathematics Subject Classifications (2000): Primary 53C40; Secondary 53C42, 53D12 相似文献
16.
The degree of freedom of a closed mechanism is the dimension of a subset M of R
n
, M being the inverse image of the unity by the closure function f : (q
1, ..., q
n
) f(q
1, ..., q
n
), where q
1, ..., q
n
are the articular coordinates. We first study the regular points for the mapping f from R
n
into the Lie group of displacements and, second, study the singularities of the mapping f. The classical theory of mechanisms considers, often implicitly, that f is a subimmersion. Here, the calculations are made in a larger case, up to second order, and the results are then slightly different. The case of such classical mechanisms as Bennett, Bricard, and Goldberg mechanisms, justify the considerations of this more general framework and the example of a Bricard mechanism is chosen as an application of the method. 相似文献
17.
Yong Seung CHO Myung Im LIM 《数学学报(英文版)》2006,22(1):115-122
Let (M, ω) be a closed symplectic 2n-dimensional manifold. Donaldson in his paper showed that there exist 2m-dimensional symplectie submanifolds (V^2m,ω) of (M,ω), 1 ≤m ≤ n - 1, with (m - 1)-equivalent inclusions. On the basis of this fact we obtain isomorphic relations between kernel of Lefschetz map of M and kernels of Lefschetz maps of Donaldson submanifolds V^2m, 2 ≤ m ≤ n - 1. Then, using this relation, we show that the flux group of M is discrete if the action of π1 (M) on π2(M) is trivial and there exists a retraction r : M→ V, where V is a 4-dimensional Donaldson submanifold. And, in the symplectically aspherical case, we investigate the flux groups of the manifolds. 相似文献
18.
Roberta Di Gennaro 《Ricerche di matematica》2009,58(2):249-262
We study the Hartshorne-Rao modules M
C
of minimal curves C in
\mathbbPN{\mathbb{P}^N} , with N ≥ 4, lying in the same liaison class of curves on a smooth rational scroll surface. We get a free minimal resolution of M
C
for some of such curves and an upper bound for Betti numbers of M
C
, for any C. 相似文献
19.
A. M. Semikhatov 《Theoretical and Mathematical Physics》2007,153(3):1597-1642
For positive integers p = k + 2, we construct a logarithmic extension of the
conformal field theory of integrable representations by taking the kernel of two fermionic screening operators in a butterfly
resolution of a three-boson realization of
. The currents W−(z) and W+(z) of a W-algebra acting in the kernel are determined by a highest-weight state of dimension 4p − 2 and charge 2p − 1 and
by a (θ=1)-twisted highest-weight state of the same dimension 4p − 2 and opposite charge −2p+1. We construct 2p W-algebra
representations, evaluate their characters, and show that together with the p−1 integrable representation characters, they
generate a modular group representation whose structure is described as a deformation of the (9p−3)-dimensional representation
R
p+1⊕ℂ2⊗R
p+1ʕR
p−1⊕ℂ2
R
p−1⊕ℂ3
R
p−1, where R
p−1 is the SL(2, ℤ)-representation on
integrable-representation characters and R
p+1 is a (p+1)-dimensional SL(2, ℤ)-representation known from the logarithmic (p, 1) model. The dimension 9p − 3 is conjecturally
the dimension of the space of torus amplitudes, and the ℂn with n = 2 and 3 suggest the Jordan cell sizes in indecomposable W-algebra modules. We show that under Hamiltonian reduction,
the W-algebra currents map into the currents of the triplet W-algebra of the logarithmic (p, 1) model.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 153, No. 3, pp. 291–346, December, 2007. 相似文献
20.
Christophe Dupont 《Mathematische Annalen》2011,349(3):509-528
Let f be an endomorphism of
\mathbbC\mathbbPk{\mathbb{C}\mathbb{P}^k} and ν be an f-invariant measure with positive Lyapunov exponents (λ
1, . . . , λ
k
). We prove a lower bound for the pointwise dimension of ν in terms of the degree of f, the exponents of ν and the entropy of ν. In particular our result can be applied for the maximal entropy measure μ. When k = 2, it implies that the Hausdorff dimension of μ is estimated by dimHm 3 [(log d)/(l1)] + [(log d)/(l2)]{{\rm dim}_\mathcal{H}\mu \geq {{\rm log} d \over \lambda_1} + {{\rm log} d \over \lambda_2}}, which is half of the conjectured formula. Our method for proving these results consists in studying the distribution of
the ν-generic inverse branches of f
n
in
\mathbbC\mathbbPk{\mathbb{C}\mathbb{P}^k} . Our tools are a volume growth estimate for the bounded holomorphic polydiscs in
\mathbbC\mathbbPk{\mathbb{C}\mathbb{P}^k} and a normalization theorem for the ν-generic inverse branches of f
n
. 相似文献
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