共查询到20条相似文献,搜索用时 31 毫秒
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We study spin structures on flat Riemannian manifolds. The main result is a necessary and sufficient condition for a flat manifold with cyclic holonomy to have a spin structure. 相似文献
3.
We define the Teichmuller pseudodistance on the space of spherical CR structures on a fixed compact manifold by using quasiconformal mappings between spherical CR manifolds. The pseudodistance is shown to be a complete distance. 相似文献
4.
Vector cross product structures on manifolds include symplectic, volume, G2- and Spin(7)-structures. We show that the knot spaces of such manifolds have natural symplectic structures, and relate instantons and branes in these manifolds to holomorphic disks and Lagrangian submanifolds in their knot spaces.For the complex case, the holomorphic volume form on a Calabi-Yau manifold defines a complex vector cross product structure. We show that its isotropic knot space admits a natural holomorphic symplectic structure. We also relate the Calabi-Yau geometry of the manifold to the holomorphic symplectic geometry of its isotropic knot space. 相似文献
5.
Wang Wei 《中国科学A辑(英文版)》2006,49(11):1523-1538
We define the Teichmüller pseudodistance on the space of spherical CR structures on a fixed compact manifold by using quasiconformal
mappings between spherical CR manifolds. The pseudodistance is shown to be a complete distance.
Dedicated to Professor Sheng GONG on the occasion of his 75th birthday 相似文献
6.
In this paper we explain how the so-called adapted complex structures can be used to associate to each compact real-analytic Riemannian manifold a family of complete Kähler-Einstein metrics and show that already one element of this family uniquely determines the original manifold. The underlying manifolds of these metrics are open disc bundles in the tangent bundle of the original Riemannian manifold.
7.
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
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We consider real analytic involutive structures 𝒱, of co-rank one, defined on a real analytic paracompact orientable manifold M. To each such structure we associate certain connected subsets of M which we call the level sets of 𝒱. We prove that analytic regularity propagates along them. With a further assumption on the level sets of 𝒱 we characterize the global analytic hypoellipticity of a differential operator naturally associated to 𝒱. As an application we study a case of tube structures. 相似文献
10.
A toric origami manifold, introduced by Cannas da Silva, Guillemin and Pires,
is a generalization of a toric symplectic manifold. For a toric symplectic manifold, its
equivariant Chern classes can be described in terms of the corresponding Delzant polytope
and the stabilization of its tangent bundle splits as a direct sum of complex line bundles.
But in general a toric origami manifold is not simply connected, so the algebraic topology
of a toric origami manifold is more difficult than a toric symplectic manifold. In this paper
they give an explicit formula of the equivariant Chern classes of an oriented toric origami
manifold in terms of the corresponding origami template. Furthermore, they prove the
stabilization of the tangent bundle of an oriented toric origami manifold also splits as a
direct sum of complex line bundles. 相似文献
11.
Maria L. Barberis Isabel G. Dotti Miatello Roberto J. Miatello 《Annals of Global Analysis and Geometry》1995,13(3):289-301
Given a manifoldM, a Clifford structure of orderm onM is a family ofm anticommuting complex structures generating a subalgebra of dimension 2
m
of End(T(M)). In this paper we investigate the existence of locally invariant Clifford structures of orderm2 on a class of locally homogeneous manifolds. We study the case of solvable extensions ofH-type groups, showing in particular that the solvable Lie groups corresponding to the symmetric spaces of negative curvature carry invariant Clifford structures of orderm2. We also show that for eachm and any finite groupF, there is a compact flat manifold with holonomy groupF and carrying a Clifford structure of orderm.Partially supported by Conicor (Argentina)Partially supported by grants from Conicet, Conicor, SECYTUNg (Argentina), and I.C.T.P. (Trieste)Partially supported by grants from Conicet, Conicor, SECYTUNC (Argentina), T.W.A.S and I.C.T.P. (Trieste) 相似文献
12.
Yuichi Shishido 《Mathematische Nachrichten》2007,280(16):1827-1833
The space of probability measures on a Riemannian manifold is endowed with the Fisher information metric. In [4] T. Friedrich showed that this space admits also Poisson structures {, }. In this note, we give directly another proof for the structure {, } being Poisson. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
13.
We first generalize the join construction described previously by the first two authors [4] for quasi-regular Sasakian-Einstein
orbifolds to the general quasi-regular Sasakian case. This allows for the further construction of specific types of Sasakian
structures that are preserved under the join operation, such as positive, negative, or null Sasakian structures, as well as
Sasakian-Einstein structures. In particular, we show that there are families of Sasakian-Einstein structures on certain 7-manifolds
homeomorphic to S
2 × S
5. We next show how the join construction emerges as a special case of Lerman’s contact fibre bundle construction [32]. In
particular, when both the base and the fiber of the contact fiber bundle are toric we show that the construction yields a
new toric Sasakian manifold. Finally, we study toric Sasakian manifolds in dimension 5 and show that any simply-connected
compact oriented 5-manifold with vanishing torsion admits regular toric Sasakian structures. This is accomplished by explicitly
constructing circle bundles over the equivariant blow-ups of Hirzebruch surfaces.
During the preparation of this work the first two authors were partially supported by NSF grants DMS-0203219 and DMS-0504367. 相似文献
14.
We study the properties of rigid geometric structures and their relation with those of finite type. The main result proves that for a noncompact simple Lie group G acting analytically on a manifold M preserving a finite volume and either a connection or a geometric structure of finite type there is a nontrivial space of globally defined Killing vector fields on the universal cover
that centralize the action of G. Several appplications of this result are provided. 相似文献
15.
本文在黎曼流形$(M,g)$的切丛$TM$ 上研究与参考文献[10]中平行的一类度量$G$以及相容的近复结构$J$.证明了切丛$TM$关于这些度量和相应的近复结构是局部共形近K\"{a}hler流形,并且把这些结构限制在单位切球丛上得到了切触度量结构的新例子. 相似文献
16.
Z. Giunashvili 《Georgian Mathematical Journal》1995,2(4):347-359
The purpose of this paper is to consider certain mechanisms of the emergence of Poisson structures on a manifold. We shall also establish some properties of the bivector field that defines a Poisson structure and investigate geometrical structures on the manifold induced by such fields. Further, we shall touch upon the dualism between bivector fields and differential 2-forms. 相似文献
17.
Stuart Armstrong 《Annals of Global Analysis and Geometry》2008,33(1):47-69
The aim of this paper and its sequel is to introduce and classify the holonomy algebras of the projective Tractor connection.
After a brief historical background, this paper presents and analyses the projective Cartan and Tractor connections, the various
structures they can preserve, and their geometric interpretations. Preserved subbundles of the Tractor bundle generate foliations
with Ricci-flat leaves. Contact- and Einstein-structures arise from other reductions of the Tractor holonomy, as do U(1) and bundles over a manifold of smaller dimension. 相似文献
18.
S. L. Druţă-Romaniuc 《Acta Mathematica Hungarica》2013,139(3):228-244
We characterize the almost product and locally product structures of general natural lift type on the cotangent bundle of a Riemannian manifold. We find the conditions under which the cotangent bundle endowed with the constructed almost product (locally product) structure and with a pseudo-Riemannian metric obtained as a general natural lift of the metric from the base manifold, is a Riemannian almost product (locally product) or an (almost) para-Hermitian manifold. Finally, by studying the closedness of the 2-form associated to the obtained (almost) para-Hermitian structure, we characterize the general natural (almost) para-Kählerian structures on the cotangent bundle. 相似文献
19.
Siegmund Kosarew Paul Lupascu 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2000,70(1):265-274
In this note we identify two complex structures (one is given by algebraic geometry, the other by gauge theory) on the set
of isomorphism classes of holomorphic bundles with section on a given compact complex manifold. In the case ofline bundles, these complex spaces are shown to be isomorphic to a space of effective divisors on the manifold.
The second author was partially supported by SNF, nr. 2000-055290.98/1. 相似文献
20.
Emmanuel Ferrand 《Geometriae Dedicata》1997,68(1):79-89
We show that the space of geodesics of a Hadamard manifold of dimension n is symplectomorphic to the cotangent bundle of the sphere of dimension n–1. This enables us to apply the techniques of symplectic geometry in cotangent bundles to the study of the extrinsic geometry of hypersurfaces and wave fronts in Hadamard manifolds. 相似文献