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The Bochner-flat cone of a CR manifold

Part of: Symplectic geometry, contact geometry Global differential geometry

Published online by Cambridge University Press:  01 May 2008

Liana David
Liana David*
Affiliation:
Institute of Mathematics of the Romanian Academy ‘Simion Stoilow’, Calea Grivitei nr. 21, Sector 1, 010702 Bucharest, Romania (email: [email protected]; [email protected])
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Abstract

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We construct a Kähler structure (which we call a generalised Kähler cone) on an open subset of the cone of a strongly pseudo-convex CR manifold endowed with a one-parameter family of compatible Sasaki structures. We determine those generalised Kähler cones which are Bochner-flat and we study their local geometry. We prove that any Bochner-flat Kähler manifold of complex dimension bigger than two is locally isomorphic to a generalised Kähler cone.

Keywords

Bochner-flat Kähler manifoldscone manifoldsCR and Sasaki manifolds

MSC classification

Secondary: 53C55: Hermitian and Kählerian manifolds 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions 53D10: Contact manifolds, general
Type
Research Article
Information
Compositio Mathematica , Volume 144 , Issue 3 , May 2008 , pp. 747 - 773
Copyright
Copyright © Foundation Compositio Mathematica 2008

References

Research supported by Centro di Ricerca Matematica ‘Ennio de Giorgi’, Scuola Normale Superiore, Pisa, Italy, and partially supported by CNCSIS grant no. GR 54/2007 code 811.