Lines on complex contact manifolds, II

Remarks on Complex Contact Manifolds

1. Statement of results. Let M be a complex manifold of complex dimension 2w + l. Let { Ui} be an open covering of M. We call M a complex contact manifold if the following conditions are satisfied: (1) On each [/,there exists a holomorphic 1-form w,such that Wi/\(do3i)n is different from zero at every point of Ui. (2) If UiC\Uj is nonempty, then there exists a nonvanishing holomorphic function ...

A Note on Homogeneous Complex Contact Manifolds

On K-contact Einstein Manifolds

The object of the present paper is to characterize K-contact Einstein manifolds satisfying the curvature condition R · C = Q(S,C), where C is the conformal curvature tensor and R the Riemannian curvature tensor. Next we study K-contact Einstein manifolds satisfying the curvature conditions C ·S = 0 and S ·C = 0, where S is the Ricci tensor. Finally, we consider K-contact Einstein manifolds sati...

On fillability of contact manifolds

The aim of this text is to give an accessible overview to some recent results concerning contact manifolds and their symplectic fillings. In particular, we work out the weakest compatibility conditions between a symplectic manifold and a contact structure on its boundary to still be able to obtain a sensible theory (Chapter II), furthermore we prove two results (Theorem A and B in Section I.4) ...

Contact Structures on 5–manifolds

Using recent work on high dimensional Lutz twists and families of Weinstein structures we show that any almost contact structure on a 5–manifold is homotopic to a contact structure.