Deformations and equitopological deformations of strongly pseudoconvex manifolds

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

Embeddability of Some Strongly Pseudoconvex Cr Manifolds

We obtain an embedding theorem for compact strongly pseudoconvex CR manifolds which are bounadries of some complete Hermitian manifolds. We use this to compactify some negatively curved Kähler manifolds with compact strongly pseudoconvex boundary. An embedding theorem for Sasakian manifolds is also derived.

Actions on Manifolds from Deformations