G-structures and Families of Isotropic Submanifolds in Complex Contact Manifolds
2007 (English)Doctoral thesis, monograph (Other academic)
We study a generalized twistor correspondence between irreducible G-structures (with torsion in general) on complex manifolds Z and moduli spaces M of deformations of isotropic homogeneous submanifolds X in complex contact manifolds Y.
For any irreducible G-structure on a complex manifold M we present an explicit construction of a contact manifold (a generalized twistor space) Y with contact line bundle L and a family F of isotropic submanifolds X in Y having M as its moduli space. We study those special properties of this family which encode geometric invariants of the original G-structure.
Conversely, given a contact manifold (Y,L) and an homogeneous isotropic submanifold X in Y satisfying certain properties, we show that the associated moduli space M of isotropic deformations of X inside Y has an induced G-structure, Gind, and then show how the invariant torsion of Gind can be read off from certain cohomology groups canonically associated with the holomorphic embedding data of X in Y.
Place, publisher, year, edition, pages
Stockholm: Matematiska institutionen , 2007. , 100 p.
Differential geometry, twistor, G-structures, deformation
Research subject Mathematics
IdentifiersURN: urn:nbn:se:su:diva-7007ISBN: 978-91-7155-490-1OAI: oai:DiVA.org:su-7007DiVA: diva2:197463
2007-09-18, sal 14, hus 5, Kräftriket, Stockholm, 13:00
Pedersen, Henrik, Professor
Merkulov, Sergei, Professor