Existence of periodic orbits for geodesible vector fields on closed 3-manifolds

Details Existence of periodic orbits for geodesible vector fields on closed 3-manifolds Existence of periodic orbits for geodesible vector fields on closed 3-manifolds

2009-04-17

arxiv.org/abs/0904.2719v1

Ergodic Theory Dynam. Systems 30 (2010), no. 6, 1817-1841

Mathematics

Dynamical Systems

Scientific paper

In this paper we deal with the existence of periodic orbits of geodesible vector fields on closed 3-manifolds. A vector field is geodesible if there exists a Riemannian metric on the ambient manifold making its orbits geodesics. In particular, Reeb vector fields and vector fields that admit a global section are geodesible. We will classify the closed 3-manifolds that admit aperiodic volume preserving real analytic geodesible vector fields, and prove the existence of periodic orbits for real analytic geodesible vector fields (not volume preserving), when the 3-manifold is not a torus bundle over the circle. We will also prove the existence of periodic orbits of C2 geodesible vector fields in some closed 3-manifolds.

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