Contact geometry and CR-structures on spheres
نویسندگان
چکیده
منابع مشابه
Contact Spheres and Hyperk¨ahler Geometry
A taut contact sphere on a 3-manifold is a linear 2-sphere of contact forms, all defining the same volume form. In the present paper we completely determine the moduli of taut contact spheres on compact left-quotients of SU(2) (the only closed manifolds admitting such structures). We also show that the moduli space of taut contact spheres embeds into the moduli space of taut contact circles. Th...
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The standard contact structure ξst on the unit sphere S 2n−1 = ∂D2n ⊂ Cn can be defined as the hyperplane field of complex tangencies. In other words, if we write J0 for the complex structure on (the tangent bundle of) C n, then ξst(p) = TpS 2n−1 ∩ J0(TpS 2n−1) for all p ∈ S2n−1. Conversely, given any contact structure ξ = kerα on S2n−1 (with α a 1-form such that α ∧ (dα)n−1 is a volume form de...
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Let Z be a compact complex (2n+1)-manifold which carries a complex contact structure, meaning a codimension-1 holomorphic sub-bundle D ⊂ TZ which is maximally non-integrable. If Z admits a Kähler-Einstein metric of positive scalar curvature, we show that it is the Salamon twistor space of a quaternion-Kähler manifold (M, g). If Z also admits a second complex contact structure D̃ 6= D, then Z = C...
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A generalization of classical theorems on the existence of sections of real, complex and quaternionic Stiefel manifolds over spheres is proved. We obtain a complete list of Lie group homomorphisms ρ : G → Gn, where Gn is one of the groups SO(n), SU(n), Sp(n) and G is one of the groups SO(k), SU(k), Sp(k), which reduce the structure group Gn in the fibre bundle Gn → Gn+1 → Gn+1/Gn.
متن کاملSasakian Geometry and Einstein Metrics on Spheres
This paper is based on a talk presented by the first author at the Short Program on Riemannian Geometry that took place at the Centre de Recherche Mathématiques, Université de Montréal, during the period June 28-July 16, 2004. It is a report on our joint work with János Kollár [BGK03] concerning the existence of an abundance of Einstein metrics on odd dimensional spheres, including exotic spher...
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ژورنال
عنوان ژورنال: Banach Center Publications
سال: 1995
ISSN: 0137-6934,1730-6299
DOI: 10.4064/-31-1-99-113