Reeb vector field

About: Reeb vector field is a research topic. Over the lifetime, 254 publications have been published within this topic receiving 4118 citations.

Finite energy cylinders of small area

Abstract: \widetilde{J} -holomorphic cylinders in \mathbb{R}\times M , where M is a contact manifold are investigated. It is shown that a sufficiently long cylinder having small area is close to a constant map, if its center action vanishes. If its center action is positive, it is close to a cylinder over a periodic orbit of the Reeb vector field, and has a well-determined shape. A compactness result is deduced, which is useful in symplectic field theory.

Classification of homogeneous almost cosymplectic three-manifolds ☆

Abstract: The purpose of this paper is to classify all simply connected homogeneous almost cosymplectic three-manifolds. We show that each such three-manifold is either a Lie group G equipped with a left invariant almost cosymplectic structure or a Riemannian product of type R × N , where N is a Kahler surface of constant curvature. Moreover, we find that the Reeb vector field of any homogeneous almost cosymplectic three-manifold, except one case, defines a harmonic map.

Nonstandard Hamiltonian structures of the Liénard equation and contact geometry

Abstract: The construction of nonstandard Lagrangians and Hamiltonian structures for Lienard equations satisfying Chiellini condition is presented and their connection to time-dependent Hamiltonian formalism...

Certain Contact Metrics as Ricci Almost Solitons

Abstract: We show that if a compact K-contact metric is a gradient Ricci almost soliton, then it is isometric to a unit sphere S 2n+1. Next, we prove that if the metric of a non-Sasakian (κ, μ)-contact metric is a gradient Ricci almost soliton, then in dimension 3 it is flat and in higher dimensions it is locally isometric to E n+1 × S n (4). Finally, a couple of results on contact metric manifolds whose metric is a Ricci almost soliton and the potential vector field is point wise collinear with the Reeb vector field of the contact metric structure were obtained.

Geometry of $H$-paracontact metric manifolds

Abstract: We introduce and study $H$-paracontact metric manifolds, that is, paracontact metric manifolds whose Reeb vector field $\xi$ is harmonic. We prove that they are characterized by the condition that $\xi$ is a Ricci eigenvector. We then investigate how harmonicity of the Reeb vector field $\xi$ of a paracontact metric manifold is related to some other relevant geometric properties, like infinitesimal harmonic transformations and paracontact Ricci solitons.