Riemannian curl in contact geometry

Sofiane Bouarroudj, Valentin Ovsienko

Research output: Contribution to journalArticle

Abstract

We consider a contact manifold with a pseudo-Riemannian metric and define a contact vector field associated with this pair of structures. We call this new differential invariant the contact Riemannian curl. We show that the contact Riemannian curl vanishes if the metric is of constant curvature and the contact structure is defined by a Killing 1-form. We also show that the contact Riemannian curl has a strong similarity with the Schwarzian derivative, since it depends only on the projective equivalence class of the metric. The subsymbol of the Laplace-Beltrami operator corresponding to a metric on a contact manifold is proportional to the contact Riemannian curl. We also show that the contact Riemannian curl vanishes on the spherical (co)tangent bundle over a Riemannian manifold.

Original languageEnglish (US)
Pages (from-to)3917-3942
Number of pages26
JournalInternational Mathematics Research Notices
Volume2015
Issue number12
DOIs
StatePublished - Jan 1 2015

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Contact Geometry
Curl
Contact
Contact Manifold
Metric
Vanish
Schwarzian Derivative
Differential Invariants
Contact Structure
Laplace-Beltrami Operator
Tangent Bundle
Riemannian Metric
Equivalence class
Riemannian Manifold
Vector Field
Directly proportional
Curvature

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Riemannian curl in contact geometry. / Bouarroudj, Sofiane; Ovsienko, Valentin.

In: International Mathematics Research Notices, Vol. 2015, No. 12, 01.01.2015, p. 3917-3942.

Research output: Contribution to journalArticle

Bouarroudj, Sofiane ; Ovsienko, Valentin. / Riemannian curl in contact geometry. In: International Mathematics Research Notices. 2015 ; Vol. 2015, No. 12. pp. 3917-3942.
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