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1.
Hyunjoo CHO 《数学物理学报(B辑英文版)》2017,37(3):695-702
It is known that any hypersurface in an almost complex space admits an almost contact manifold [11, 14]. In this article we show that a hyperplane in an almost contact manifold has an almost complex structure. Along with this result, we explain how to determine when an almost contact structure induces a contact structure, followed by examples of a manifold with a closed G2-structure. 相似文献
2.
Luigi Vezzoni 《Israel Journal of Mathematics》2010,178(1):253-267
In this paper we generalize the definition of symplectic connection to the contact case. It turns out that any odd-dimensional
manifold equipped with a contact form admits contact connections and that any Sasakian structure induces a canonical contact
connection. Furthermore (as in the symplectic case), any contact connection induces an almost CR structure on the contact
twistor space which is integrable if and only if the curvature of the connection is of Ricci-type. 相似文献
3.
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
4.
We give a homotopy classification of foliations on open contact manifolds whose leaves are contact submanifolds of the ambient space. The result is an extension of Haefliger’s classification of foliations on open manifold in the contact setting. While proving the main theorem, we also prove a result on equidimensional isocontact immersions on open contact manifolds. 相似文献
5.
We study ball-homogeneity, curvature homogeneity, natural reductivity, conformal flatness and ϕ-symmetry for three-dimensional
contact metric manifolds. Several classification results are given.
Member of G.N.S.A.G.A.
Supported by funds of the M.U.R.S.T. 相似文献
6.
7.
We study the Riemannian geometry of contact manifolds with respect to a fixed admissible metric, making the Reeb vector field unitary and orthogonal to the contact distribution, under the assumption that the Levi–Tanaka form is parallel with respect to a canonical connection with torsion. 相似文献
8.
CĂtĂlin Gherghe 《Rendiconti del Circolo Matematico di Palermo》2000,49(3):415-424
In this paper we shall study some classes of harmonic maps on Trans-Sasakian manifolds. 相似文献
9.
We construct the CR invariant canonical contact form can(J) on scalar positive spherical CR manifold (M,J), which is the CR analogue of canonical metric on locally conformally flat manifold constructed by Habermann and Jost. We also construct another canonical contact form on the Kleinian manifold ()/, where is a convex cocompact subgroup of AutCRS2n+1=PU(n+1,1) and () is the discontinuity domain of . This contact form can be used to prove that ()/ is scalar positive (respectively, scalar negative, or scalar vanishing) if and only if the critical exponent ()<n (respectively, ()>n, or ()=n). This generalizes Nayatanis result for convex cocompact subgroups of SO(n+1,1). We also discuss the connected sum of spherical CR manifolds. 相似文献
10.
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
11.
12.
This paper applies K-homology to solve the index problem for a class of hypoelliptic (but not elliptic) operators on contact manifolds. K-homology is the dual theory to K-theory. We explicitly calculate the K-cycle (i.e., the element in geometric K-homology) determined by any hypoelliptic Fredholm operator in the Heisenberg calculus. The index theorem of this paper precisely indicates how the analytic versus geometric K-homology setting provides an effective framework for extending formulas of Atiyah–Singer type to non-elliptic Fredholm operators. 相似文献
13.
ZHANG YongBing 《中国科学A辑(英文版)》2009,(8)
We use the contact Yamabe flow to find solutions of the contact Yamabe problem on K-contact manifolds. 相似文献
14.
《Expositiones Mathematicae》2022,40(2):231-248
We prove that Legendrian and transverse links in overtwisted contact structures having overtwisted complements can be classified coarsely by their classical invariants. We further prove that any coarse equivalence class of loose links has support genus zero and construct examples to show that the converse does not hold. 相似文献
15.
Charles P. Boyer Krzysztof Galicki 《Proceedings of the American Mathematical Society》2001,129(8):2419-2430
We show that every K-contact Einstein manifold is Sasakian-Einstein and discuss several corollaries of this result.
16.
A notion of almost contact metric statistical structure is introduced and thereby contact metric and K-contact statistical structures are defined. Furthermore a necessary and sufficient condition for a contact metric statistical manifold to admit K-contact statistical structure is given. Finally, the condition for an odd-dimensional statistical manifold to have K-contact statistical structure is expressed. 相似文献
17.
18.
19.
The canonical-type connection on the almost contact manifolds with B-metric is constructed. It is proved that its torsion is invariant with respect to a subgroup of the general conformal transformations of the almost contact B-metric structure. The basic classes of the considered manifolds are characterized in terms of the torsion of the canonical-type connection. 相似文献
20.
D. Chinea 《Acta Mathematica Hungarica》2010,126(4):352-365
We study (φ,φ′)-holomorphic maps between almost contact metric manifolds, in particular horizontally conformal (φ,φ′)-holomorphic submersions, and obtain some criteria for the harmonicity of such maps. 相似文献