Related papers: The geometry of marked contact Engel structures

We present Twisted Edges, a unified framework for designing Linked Knot (LK) structures using labeled non-manifold surface meshes. While the concept of edge twists, originating in topological graph theory, is foundational to these designs,…

We establish a twistor correspondence between a cuspidal cubic curve in a complex projective plane, and a co-calibrated homogeneous $G_2$ structure on the seven--dimensional parameter space of such cubics. Imposing the Riemannian reality…

In this paper we construct non-simply connected contact manifolds $M$ of dimension $\geq5$ such that $M\times S^1$ does not admit a symplectic structure.

A 4-dimensional Riemannian manifold M, equipped with an additional tensor structure S, whose fourth power is minus identity, is considered. The structure S has a skew-circulant matrix with respect to some basis of the tangent space at a…

Parabolic almost conformally symplectic structures were introduced in the first part of this series of articles as a class of geometric structures which have an underlying almost conformally symplectic structure. If this underlying…

We discuss a correspondence between certain contact pairs on the one hand, and certain locally conformally symplectic forms on the other. In particular, we characterize these structures through suspensions of contactomorphisms. If the…

Let $M$ be a three-dimensional contact manifold and $\psi:D\setminus\{0\}\to M\times{\Bbb R}$ a finite-energy pseudoholomorphic map from a punctured disc in ${\Bbb C}$, that is asymptotic to a periodic orbit of the Reeb vector field. This…

This paper investigates the transfer of classical geometric structures from a smooth manifold $M$ to its Weil bundle $(M^\mathbf A, \tilde\pi_M, M)$ associated with a Weil algebra $\mathbf A$. We show that various structures including…

Let $X$ be a quasi-projective curve, compactified to $(Y,D)$ with $X=Y-D$. We construct a Deligne-Hitchin twistor space out of moduli spaces of framed $\lambda$-connections of rank $2$ over $Y$ with logarithmic singularities and…

An Engel manifold is a 4-manifold with a completely non-integrable 2-distribution called Engel structure. I research the functorial relation between Engel manifolds and Contact 3-orbifolds. And I construct an Engel manifold that the…

We study a modified version of Lerman-Whitehouse Menger-like curvature defined for m+2 points in an n-dimensional Euclidean space. For 1 <= l <= m+2 and an m-dimensional subset S of R^n we also introduce global versions of this discrete…

We show that the pre-order defined on the category of contact manifolds by arbitrary symplectic cobordisms is considerably less rigid than its counterparts for exact or Stein cobordisms: in particular, we exhibit large new classes of…

In this paper, we compute contact homology of some quasi-regular contact structures, which admit Hamiltonian actions of Reeb type of Lie groups. We will discuss the toric contact case, (where the torus is of Reeb type), and the case of…

We construct open book structures on all moment-angle manifolds and describe the topology of their leaves and bindings under certain restrictions. II. We also show, using a recent deep result about contact forms due to Borman, Eliashberg…

We extend the notion of a Sasakian structure from the classical setting of a cooriented contact manifold, where it is given by a compatibility between a contact form $\eta$ and a Riemannian metric $g_M$ on $M$, to the case of an arbitrary…

Let L->M be a Hermitian line bundle over a compact manifold. Write S for the space of all unitary connections in L whose curvatures define symplectic forms on M and G for the group of unitary bundle isometries of L, which acts on S by…

We give a sufficient condition for an $\mathbb{S}^1$-bundle over a $3$-manifold to admit an immersion (or embedding) into $\mathbb{C}^3$ so that its complex tangencies define an Engel structure. In particular, every oriented…

We study pairs of Engel structures on four-manifolds whose intersection has constant rank one and which define the same even contact structure, but induce different orientations on it. We establish a correspondence between such pairs of…

We develop a systematic approach to contact and Jacobi structures on graded supermanifolds. In this framework, contact structures are interpreted as symplectic principal GL(1,R)-bundles. Gradings compatible with the GL(1,R)-action lead to…

This thesis focuses on developing "stacky" versions of contact structures, extending the classical notion of contact structures on manifolds. A fruitful approach is to study contact structures using line bundle-valued $1$-forms.…