Contact structures on algebraic 5-dimensional manifolds

Special lines on contact manifolds

In a series of two articles Kebekus studied deformation theory of minimal rational curves on contact Fano manifolds. Such curves are called contact lines. Kebekus proved that a contact line through a general point is necessarily smooth and has a fixed standard splitting type of the restricted tangent bundle. In this paper we study singular contact lines and those with special splitting type. We provide restrictions on the families of such lines, and on contact Fano manifolds which have reducible varieties of minimal rational tangents. We also show that the results about singular lines naturall…

Quasi-complete homogeneous contact manifold associated to a cubic form

Starting from a cubic form, we give a general construction of a quasi-complete homogeneous manifold endowed with a natural contact structure. We show that it can be compactified into a projective contact manifold if and only if the cubic form is the determinant of a simple cubic Jordan algebra.

Duality and integrability on contact Fano manifolds

We address the problem of classification of contact Fano manifolds. It is conjectured that every such manifold is necessarily homogeneous. We prove that the Killing form, the Lie algebra grading and parts of the Lie bracket can be read from geometry of an arbitrary contact manifold. Minimal rational curves on contact manifolds (or contact lines) and their chains are the essential ingredients for our constructions. Along the way we collect several facts about bundles of projective lines admitting a contractible section, which might be of independent interest.

紧致凯勒接触流形

Compact Kähler contact manifolds

论文证明非射影紧致凯勒接触流形形式为P T_Y，其中Y为紧致凯勒流形。

H-principle for complex contact structures on Stein manifolds

In this paper we introduce the notion of a formal complex contact structure on an odd dimensional complex manifold. Our main result is that every formal complex contact structure on a Stein manifold $X$ is homotopic to a holomorphic contact structure on a Stein domain $Ω\subset X$ which is diffeotopic to $X$. We also prove a parametric h-principle in this setting, analogous to Gromov's h-principle for contact structures on smooth open manifolds. On Stein threefolds we obtain a complete homotopy classification of formal complex contact structures. Our methods also furnish a parametric h-princip…

Slant submanifolds of lorentzian almost contact manifolds

In this paper we study slant submanifolds of Lorentzian almost contact manifolds. We have taken the submanifold as a space like and then defined the slant angle on a submanifold and thus we extended the results of A. Lotta (Slant submanifolds in contact geometry [8]) and M. A. Khan et. al. (Slant submanifolds of Lorentzian Paracontact manifolds [7]) in this new setting.