Complex structures on open manifolds

Manifolds with Many Complex Structures

Open Book Decompositions for Contact Structures on Brieskorn Manifolds

In this paper, we give an open book decomposition for the contact structures on some Brieskorn manifolds, in particular for the contact structures of Ustilovsky. The decomposition uses right-handed Dehn twists as conjectured by Giroux. 0. Introduction At the ICM of 2002 Giroux announced some of his results concerning a correspondence between contact structures on manifolds and open book structu...

Algebraic Structures on Hyperkähler Manifolds Algebraic Structures on Hyperkähler Manifolds

Let M be a compact hyperkähler manifold. The hy-perkähler structure equips M with a set R of complex structures parametrized by CP 1 , called the set of induced complex structures. It was known previously that induced complex structures are non-algebraic, except may be a countable set. We prove that a countable set of induced complex structures is algebraic, and this set is dense in R. A more g...

Orthogonal complex structures on certain Riemannian 6-manifolds∗

It is shown that the Hermitian-symmetric space CP1 × CP1 × CP1 and the flag manifold F1,2 endowed with any left invariant metric admit no compatible integrable almost complex structures (even locally) different from the invariant ones. As an application it is proved that any stable harmonic immersion from F1,2 equipped with an invariant metric into an irreducible Hermitian symmetric space of co...

Poisson Structures on Complex Flag Manifolds Associated with Real Forms

For a complex semisimple Lie group G and a real form G0 we define a Poisson structure on the variety of Borel subgroups of G with the property that all G0-orbits in X as well as all Bruhat cells (for a suitable choice of a Borel subgroup of G) are Poisson submanifolds. In particular, we show that every non-empty intersection of a G0-orbit and a Bruhat cell is a regular Poisson manifold, and we ...