Global stability for Holomorphic Foliations on Kaehler manifolds

Foliations on hypersurfaces in holomorphic symplectic manifolds

Let Y be a hypersurface in a 2n-dimensional holomorphic symplectic manifold X. The restriction σ|Y of the holomorphic symplectic form induces a rank one foliation on Y . We investigate situations where this foliation has compact leaves; in such cases we obtain a space of leaves Y/F which has dimension 2n − 2 and admits a holomorphic symplectic form.

Lecture on Kaehler manifolds

Strongly Fillable Contact Manifolds and J–holomorphic Foliations

We prove that every strong symplectic filling of a planar contact manifold admits a Lefschetz fibration over a disk that restricts to any given planar open book at the boundary. It follows that strongly fillable planar contact structures are also Stein fillable. Using similar methods, involving foliations by J–holomorphic curves, we construct a Lefschetz fibration over the annulus for any stron...

A Measurable Stability Theorem for Holomorphic Foliations Transverse to Fibrations

Ricci tensor for $GCR$-lightlike submanifolds of indefinite Kaehler manifolds

We obtain the expression of Ricci tensor for a $GCR$-lightlikesubmanifold of indefinite complex space form and discuss itsproperties on a totally geodesic $GCR$-lightlike submanifold of anindefinite complex space form. Moreover, we have proved that everyproper totally umbilical $GCR$-lightlike submanifold of anindefinite Kaehler manifold is a totally geodesic $GCR$-lightlikesubmanifold.