Related papers: Conformal great circle flows on the three-sphere

The aim of this article is to investigate the presence of a conformal vector $\xi$ with conformal factor $\rho$ on a compact Riemannian manifold $M$ with or without boundary $\partial M$. We firstly prove that a compact Riemannian manifold…

Let M denote a compact, oriented 3-manifold and let a denote a contact 1-form on M. This article proves that the vector field that generates the kernel of the 2-form da has at least one closed, integral curve.

Let $(S,\Phi)$ be a pair of a closed oriented surface and $\Phi$ be a real analytic flow with finitely many singularities. Let $x$ be a point of $S$ with the polycycle $\omega$-limit set $\omega(x)$. In this paper we give topological…

In this paper we define and study pseudoholomorphic vector bundles structures, particular cases of which are tangent and normal bundle almost complex structures. These are intrinsically related to the Gromov D-operator. As an application we…

We complete the proof of the Generalized Smale Conjecture, apart from the case of $RP^3$, and give a new proof of Gabai's theorem for hyperbolic 3-manifolds. We use an approach based on Ricci flow through singularities, which applies…

This paper helps to clarify the status of cylindrical contact homology, a conjectured contact invariant introduced by Eliashberg, Givental, and Hofer in 2000. We explain how heuristic arguments fail to yield a well-defined homological…

We study non-degenerate Reeb flows arising from perfect contact forms, i.e., the forms with vanishing contact homology differential. In particular, we obtain upper bounds on the number of simple closed Reeb orbits for such forms on a…

A recent paper [CGT] studies the evolution of star-shaped mean convex hypersurfaces of the Euclidean space by a class of nonhomogeneous expanding curvature flows. In the present paper we consider the same problem in the real, complex and…

In this article, we characterize two kinds of exceptional orbits of the geodesic flow associated with the Modular surface in terms of a two-parameter family of continued fraction expansion of endpoints of the lifts to the hyperbolic plane…

We propose a contact-topological approach to the spatial circular restricted three-body problem, for energies below and slightly above the first critical energy value. We prove the existence of a circle family of global hypersurfaces of…

We discuss canonical transformations relating well-known geodesic flows on the cotangent bundle of the sphere with a set of geodesic flows with quartic invariants. By adding various potentials to the corresponding geodesic Hamiltonians, we…

For the model of a compressible barotropic fluid on a two dimensional rotating Riemmanian manifold we discuss a special class of smooth solutions having a form of a steady non-singular vortex moving with a bearing field. The model can be…

We construct, for any given positive integer $n$, Reeb flows on contact integral homology 3-spheres which do not admit global surfaces of section with fewer than $n$ boundary components. We use a connected sum operation for open books to…

We introduce the notion of conformal trajectories in three-dimensional Riemannian manifolds $M^3$. Given a conformal vector field $V\in\mathfrak{X}(M^3)$, a conformal trajectory of $V$ is a regular curve $\gamma$ in $M^3$ satisfying…

We investigate the local geometry of a pair of independent contact structures on 3-manifolds under maps that independently preserve each contact structure. We discover that such maps are homotheties on the contact 1-forms and we discover…

Let G be a Lie goup, let M and N be smooth connected G-manifolds, let f be a smooth G-map from M to N, and let P denote the fiber of f. Given a closed and equivariantly closed relative 2-form for f with integral periods, we construct the…

Investigation of the effects of a contact surgery construction and of invariance of contact homology reveals a rich new field of inquiry at the intersection of dynamical systems and contact geometry. We produce contact 3-flows not…

We study natural variations of the G2 structure {\sigma}_0 \in {\Lambda}^3_+ existing on the unit tangent sphere bundle SM of any oriented Riemannian 4-manifold M. We find a circle of structures for which the induced metric is the usual…

We present a variety of geometrical and combinatorial tools that are used in the study of geometric structures on surfaces: volume, contact, symplectic, complex and almost complex structures. We start with a series of local rigidity results…

We show that any co-oriented closed contact manifold of dimension at least five admits a contact form such that the contact volume is arbitrarily small but the Reeb flow admits a global hypersurface of section with the property that the…