Complex parallelisable manifolds and their small deformations

Statistical cosymplectic manifolds and their submanifolds

    In ‎this ‎paper‎, we introduce statistical cosymplectic manifolds and investigate some properties of their tensors. We define invariant and anti-invariant submanifolds and study invariant submanifolds with normal and tangent structure vector fields. We prove that an invariant submanifold of a statistical cosymplectic manifold with tangent structure vector field is a cosymplectic and minimal...

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...

Actions on Manifolds from Deformations

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