On characteristic foliations of metric contact-symplectic structures
Abstract
We study compatible and associated metrics for a contact-symplectic pair \((\eta, \omega)\) on a manifold. We show that the integral curves of the Reeb vector field are geodesics for any compatible metric. We prove that all associated metrics share a common volume element, which we give explicitly. When the characteristic foliations of \(\eta\) and \(\omega\) are orthogonal with respect to an associated metric, their leaves, as well as those of the characteristic foliation of \(d\eta\), are minimal. We construct explicit examples on nilpotent Lie groups and nilmanifolds where the characteristic foliations are not both totally geodesic.
Fields of Study & Subjects
Advanced Differential Geometry Research
Geometric Analysis and Curvature Flows
Geometric and Algebraic Topology
Publication details
- Journal / source
- Cubo
- Volume
- 28
- Issue
- 3
- Pages
- 437–437
- Publication date
- 1 September 2026
- Language
- EN