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1.
Two constructions of contact manifolds are presented: (i) products of S
1 with manifolds admitting a suitable decomposition into two exact symplectic pieces and (ii) fibre connected sums along isotropic
circles. Baykur has found a decomposition as required for (i) for all closed, oriented 4-manifolds. As a corollary, we can
show that all closed, oriented 5-manifolds that are Cartesian products of lower-dimensional manifolds carry a contact structure.
For symplectic 4-manifolds we exhibit an alternative construction of such a decomposition; this gives us control over the
homotopy type of the corresponding contact structure. In particular, we prove that
\mathbb CP2×S1{{\mathbb {CP}}^2\times S^1} admits a contact structure in every homotopy class of almost contact structures. The existence of contact structures is also
established for a large class of 5-manifolds with fundamental group
\mathbbZ2{{\mathbb{Z}}_2} . 相似文献
2.
We establish the existence of smooth invariant center manifolds for the nonuniformly partially hyperbolic trajectories of a diffeomorphism in a Banach space. This means that the differentials of the diffeomorphism along the trajectory admit a nonuniform exponential trichotomy. We also consider the more general case of sequences of diffeomorphisms, which corresponds to a nonautonomous dynamics with discrete time. In addition, we obtain an optimal regularity for the center manifolds: if the diffeomorphisms are of class Ck then the manifolds are also of class Ck. As a byproduct of our approach we obtain an exponential control not only for the trajectories on the center manifolds, but also for their derivatives up to order k. 相似文献
3.
Amalendu Ghosh 《Acta Mathematica Hungarica》2010,129(4):357-367
We study holomorphically planar conformal vector fields (HPCV) on contact metric manifolds under some curvature conditions.
In particular, we have studied HPCV fields on (i) contact metric manifolds with pointwise constant ξ-sectional curvature (under this condition M is either K-contact or V is homothetic), (ii) Einstein contact metric manifolds (in this case M becomes K contact), (iii) contact metric manifolds with parallel Ricci tensor (under this condition M is either K-contact Einstein or is locally isometric to E
n+1×S
n
(4)). 相似文献
4.
Let A be a unitary commutative complete locally m-convex C
*-algebra. We prove that the projective finitely generated A-modules admit differentiable A-valued bump-functions. Then we
consider manifolds modelled on such modules and we prove that locally defined differentiable mappings and sections on these
manifolds extend to global ones.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
5.
Anatoly Libgober 《中国科学A辑(英文版)》2009,52(12):2688-2698
We discuss the properties of complex manifolds having rational homology of S
1 × S
2n−1 including those constructed by Hopf, Kodaira and Brieskorn-van de Ven. We extend certain previously known properties of cohomology
of bundles on such manifolds. As an application we consider degeneration of Hodge-de Rham spectral sequence in this non Kahler
setting. 相似文献
6.
Wei Wang 《Annali di Matematica Pura ed Applicata》2007,186(2):359-380
By constructing normal coordinates on a quaternionic contact manifold M, we can osculate the quaternionic contact structure at each point by the standard quaternionic contact structure on the quaternionic
Heisenberg group. By using this property, we can do harmonic analysis on general quaternionic contact manifolds, and solve
the quaternionic contact Yamabe problem on M if its Yamabe invariant satisfies λ(M) < λ(ℍ
n
).
Mathematics Subject Classification (2000) 53C17, 53D10, 35J70 相似文献
7.
S. Azarmi 《Russian Mathematics (Iz VUZ)》2012,56(1):76-78
In this paper we consider a category of manifolds over the algebra of even degree exterior forms on ℝ
N
. We give examples of suchmanifolds. We explicitly find elements of the pseudogroup of differentiable transformations and
demonstrate that on any differentiable manifold there exist affine foliations. 相似文献
8.
Stefan Kebekus Thomas Peternell Andrew J. Sommese Jarosław A. Wiśniewski 《Inventiones Mathematicae》2000,142(1):1-15
The present work is concerned with the study of complex projective manifolds X which carry a complex contact structure. In the first part of the paper we show that if K
X
is not nef, then either X is Fano and b
2(X)=1, or X is of the form ℙ(T
Y
), where Y is a projective manifold. In the second part of the paper we consider contact manifolds where K
X
is nef.
Oblatum 15-X-1999 & 3-II-2000?Published online: 8 May 2000 相似文献
9.
Constantin C?lin 《Mediterranean Journal of Mathematics》2011,8(2):191-206
On an odd dimensional manifold, we define a structure which generalizes several known structures on almost contact manifolds,
namely Sasakian, trans-Sasakian, quasi-Sasakian, Kenmotsu and cosymplectic structures. This structure, hereinafter called
a generalized quasi-Sasakian, shortly G.Q.S. structure, is defined on an almost contact metric manifold and satisfies an additional
condition. Then we consider a distribution D1{\mathcal{D}_{1}} wich allows a suitable decomposition of the tangent bundle of a G.Q.S. manifold. Necessary and sufficient conditions for
the normality of the complemented framed structure on the distribution D1{\mathcal{D}_{1}} defined on a G.Q.S manifold are studied. The existence of the foliation on G.Q.S. manifolds and of bundle-like metrics are
also proven. It is shown that under certain circumstances a new foliation arises and its properties are investigated. Some
examples illustrating these results are given in the final part of this paper. 相似文献
10.
We consider a Yamabe-type problem on locally conformally flat compact manifolds with boundary. The main technique we used
is to derive boundary C
2 estimates directly from boundary C
0 estimates. We will control the third derivatives on the boundary instead of constructing a barrier function. This result
is a generalization of the work by Escobar. 相似文献
11.
Domenico Perrone 《Mathematische Zeitschrift》2009,263(1):125-147
It is well known that a Hopf vector field on the unit sphere S
2n+1 is the Reeb vector field of a natural Sasakian structure on S
2n+1. A contact metric manifold whose Reeb vector field ξ is a harmonic vector field is called an H-contact manifold. Sasakian and K-contact manifolds, generalized (k, μ)-spaces and contact metric three-manifolds with ξ strongly normal, are H-contact manifolds. In this paper we study, in dimension three, the stability with respect to the energy of the Reeb vector
field ξ for such special classes of H-contact manifolds (and with respect to the volume when ξ is also minimal) in terms of Webster scalar curvature. Finally, we extend for the Reeb vector field of a compact K-contact (2n+1)-manifold the obtained results for the Hopf vector fields to minimize the energy functional with mean curvature correction.
Supported by funds of the University of Lecce and M.I.U.R.(PRIN). 相似文献
12.
Amalendu Ghosh 《Annals of Global Analysis and Geometry》2009,35(4):431-441
In this paper we study Einstein-Weyl structures in the framework of contact metric manifolds. First, we prove that a complete
K-contact manifold admitting both the Einstein-Weyl structures W
± = (g, ±ω) is Sasakian. Next, we show that a compact contact metric manifold admitting an Einstein-Weyl structure is either K-contact or the dual field of ω is orthogonal to the Reeb vector field, provided the Reeb vector field is an eigenvector of the Ricci operator. We also prove
that a contact metric manifold admitting both the Einstein-Weyl structures and satisfying is either K-contact or Einstein. Finally, a couple of results on contact metric manifold admitting an Einstein-Weyl structure W = (g, f
η) are presented.
相似文献
13.
Domenico Perrone 《Acta Mathematica Hungarica》2013,138(1-2):102-126
We investigate almost contact metric manifolds whose Reeb vector field is a harmonic unit vector field, equivalently a harmonic section. We first consider an arbitrary Riemannian manifold and characterize the harmonicity of a unit vector field ??, when ??? is symmetric, in terms of Ricci curvature. Then, we show that for the class of locally conformal almost cosymplectic manifolds whose Reeb vector field ?? is geodesic, ?? is a harmonic section if and only if it is an eigenvector of the Ricci operator. Moreover, we build a large class of locally conformal almost cosymplectic manifolds whose Reeb vector field is a harmonic section. Finally, we exhibit several classes of almost contact metric manifolds where the associated almost contact metric structures ?? are harmonic sections, in the sense of Vergara-Diaz and Wood?[25], and in some cases they are also harmonic maps. 相似文献
14.
We consider a natural condition determining a large class of almost contact metric structures. We study their geometry, emphasizing that this class shares several properties with contact metric manifolds. We then give a complete classification of left‐invariant examples on three‐dimensional Lie groups, and show that any simply connected homogeneous Riemannian three‐manifold admits a natural almost contact structure having g as a compatible metric. Moreover, we investigate left‐invariant CR structures corresponding to natural almost contact metric structures. 相似文献
15.
Goutam Mukherjee 《Proceedings Mathematical Sciences》1995,105(4):381-391
We consider certain natural (ℤ2)n actions on real Grassmann and flag manifolds andS
1 actions on complex Grassmann manifolds with finite stationary point sets and determine completely which of them bound equivariantly. 相似文献
16.
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
17.
Viorel Vâjâitu 《Journal of Geometric Analysis》1998,8(1):163-177
We consider bounded and q-complete domains in
C
n
with
C
2
boundary. We show that they enjoy special q-convexity properties, i.e., they admit q-convex bounded exhaustion function and
their closure do have a fundamental system of (q + 1)-complete neighborhoods. Moreover, we produce an example of a q- complete domain (which we called the q-worm) with smooth boundary
whose closure does not possess a fundamental system of q-complete neighborhoods.
Finally, extensions of these results to p-complete manifolds are given. 相似文献
18.
Christian Br 《Mathematische Nachrichten》1999,201(1):7-35
If G is the structure group of a manifold M it is shown how a certain ideal in the character ring of G corresponds to the set of geometric elliptic operators on M. This provides a simple method to construct these operators. For classical structure groups like G = O(n) (Riemannian manifolds), G = SO(n) (oriented Riemannian manifolds), G = U(m) (almost complex manifolds), G = Spin(n) (spin manifolds), or G = Spinc(n) (spinc manifolds) this yields well known classical operators like the Euler—deRham operator, signature operator, Cauchy—Riemann operator, or the Dirac operator. For some less well studied structure groups like Spinh(n) or Sp(q)Sp(1) we can determine the corresponding operators. As applications, we obtain integrality results for such manifolds by applying the Atiyah—Singer Index Theorem to these operators. Finally, we explain how immersions yield interesting structure groups to which one can apply this method. This yields lower bounds on the codimension of immersions in terms of topological data of the manifolds involved. 相似文献
19.
We consider almost contact metric hypersurfaces of almost Hermitian manifolds of class W3 (in the Gray–Hervella terminology). We establish a criterion for minimality of such hypersurfaces in the case when the contact metric structure is cosymplectic. 相似文献
20.
Luis Barreira Claudia Valls 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(5):1616-1627
We establish the existence of smooth center manifolds under sufficiently small perturbations of an impulsive linear equation. In particular, we obtain the C1 smoothness of the manifolds outside the jumping times. We emphasize that we consider the general case of nonautonomous equations for which the linear part has a nonuniform exponential trichotomy. 相似文献