Related papers: Contact manifolds and generalized complex structur…

This paper contains theory on two related topics relevant to manifolds of normally hyperbolic singularities. First, theorems on the formal and $ C^k $ normal forms for these objects are proved. Then, the theorems are applied to give…

In this note we study contact structures on 5-dimensional manifolds. We give a complete answer under the assumption that the Abundance conjecture holds in dimension 5.

We study contact structures on smooth complex projective varieties with a simple normal crossing divisor, generalizing some well-known results concerning the non-logarithmic case. In particular, we describe the structure of elementary log…

We reexamine the relation between contact structures on supermanifolds and supersymmetric mechanics in the superspace formulation. This allows one to use the language of contact geometry when dealing with the d = 1, N = 2 super-Poincare…

In this article we classify up to isotopy tight contact structures on Seifert manifolds over the torus with one singular fibre.

The aim of this paper is to present the main constructions of the substructures of an almost groupoid and to discuss their basic properties. The definitions and properties concerning these new algebraic constructions extend to almost…

In this paper we extend the almost complex Poisson structures from almost complex manifolds to almost complex Lie algebroids. Examples of such structures are also given and the almost complex Poisson morphisms of almost complex Lie…

In this article we study a class of normal{\theta}complex{\theta}contact{\theta}metric{\theta}manifold which is called a complex Sasakian manifold. This kind of manifold has a globally defined complex contact form and normal complex contact…

The study of harmonicity for almost contact metric structures was initiated by Vergara-D\'iaz and Wood and continued by Gonz\'alez-D\'avila and the present author. By using the intrinsic torsion and some restriction on the type of almost…

Iterated planar contact manifolds are a generalization of three dimensional planar contact manifolds to higher dimensions. We study some basic topological properties of iterated planar contact manifolds and discuss several examples and…

The notions of a twistor space of a contact manifold and a contact connection on such a manifold have been introduced by L. Vezzoni as extensions of the corresponding notions in the case of a symplectic manifold. Given a contact connection…

With the goal to study and better understand algebraic Anosov actions of $\mathbb R^k$, we develop a higher codimensional analogue of the contact distribution on odd dimensional manifolds, call such structure a generalized $k$-contact…

We show that the canonical contact structure on the link of a normal complex singularity is universally tight. As a corollary we show the existence of closed, oriented, atoroidal 3-manifolds with infinite fundamental groups which carry…

Twists of contact structures in dimension 3 and higher are studied in this paper from a viewpoint of contact round surgery. Three kinds of new modifications of contact structures which are higher-dimensional generalizations of the…

A Sasaki-like almost contact complex Riemannian manifold is defined as an almost contact complex Riemannian manifold which complex cone is a holomorphic complex Riemannian manifold. Explicit compact and non-compact examples are given. A…

Almost contact manifolds with B-metric are considered. Of special interest are the so-called vertical classes of the almost contact B-metric manifolds. Curvature properties of these manifolds are studied. An example of 5-dimensional…

Weak contact metric manifolds, i.e., the linear complex structure on the contact distribution is replaced by a nonsingular skew-symmetric tensor, defined by the author and R. Wolak, allowed a new look at the theory of contact manifolds. In…

We establish some fundamental relations between Dirac subbundles $L$ for the generalized Courant algebroid $(A\oplus A^{\ast}, \phi+W)$ over a differentiable manifold $M$ and the associated Dirac subbubndles $\tilde{L}$ for the…

We give a normal form for families of 3-dimensional Poisson structures. This allows us to classify singularities with nonzero 1-jet and typical bifurcations. The Appendix contains corollaries on classification of families of integrable…

Systems of partial differential equations which appear in classical field theories can be studied geometrically using different geometrical structures, for example, k-symplectic geometry, k-cosymplectic geometry, multisymplectic geometry,…