Deformations of Oka manifolds

An Oka Principle for Stein G-manifolds

Let G be a reductive complex Lie group acting holomorphically on Stein manifolds X and Y . Let pX : X → QX and pY : Y → QY be the quotient mappings. Assume that we have a biholomorphism Q := QX → QY and an open cover {Ui} of Q and G-biholomorphisms Φi : p −1 X (Ui)→ p −1 Y (Ui) inducing the identity on Ui. There is a sheaf of groups A on Q such that the isomorphism classes of all possible Y is ...

Deformations in G2 Manifolds

Here we study the deformations of associative submanifolds inside a G2 manifold M 7 with a calibration 3-form φ. A choice of 2-plane field Λ on M (which always exists) splits the tangent bundle of M as a direct sum of a 3-dimensional associate bundle and a complex 4-plane bundle TM = E ⊕ V, and this helps us to relate the deformations to SeibergWitten type equations. Here all the surveyed resul...

Deformations of Holomorphic Poisson Manifolds

An unobstructedness theorem is proved for deformations of compact holomorphic Poisson manifolds and applied to a class of examples. These include certain rational surfaces and Hilbert schemes of points on Poisson surfaces. We study in particular the Hilbert schemes of the projective plane and show that a generic deformation is determined by two parameters—an elliptic curve and a translation on ...

Deformations of Hyperbolic Cone Manifolds

We show that any compact orientable hyperbolic cone manifold with cone angles at most can be continuously deformed to a complete hyperbolic manifold homeomorphic to the complement of the singularity This together with the local rigidity by Hodgson and Kerckho implies the global rigidity for compact orientable hyperbolic cone manifolds under the same angle assumption

Actions on Manifolds from Deformations