On vector fields having properties of Reeb fields

TL;DR

This paper explores the construction of vector fields with properties similar to Reeb fields, demonstrating that all closed oriented odd-dimensional manifolds admit geodesible vector fields.

Contribution

It proves that every closed oriented odd-dimensional manifold can support geodesible vector fields with Reeb-like properties.

Findings

All closed oriented odd-dimensional manifolds have geodesible vector fields.

Constructed vector fields exhibit properties characteristic of Reeb vector fields.

Provides new methods for constructing Reeb-like vector fields on manifolds.

Abstract

We study constructions of vector fields with properties which are characteristic to Reeb vector fields of contact forms. In particular, we prove that all closed oriented odd-dimensional manifold have geodesible vector fields.