English

Surfaces in a strict Walker 3-manifold that contain non-null curves with zero torsion

Differential Geometry 2025-08-04 v3

Abstract

Given a non-null curve γ\gamma in a strict Walker 3-manifold, first we show that (locally) γ\gamma lies in a flat cylinder with a null axis. Secondly, we construct an example of such a curve γ\gamma and such a cylinder SS that contains γ\gamma . In particular, the hypothesis that SS is totally geodesic has some consequence on the geometry of the ambient Walker 3-manifold.

Keywords

Cite

@article{arxiv.2507.22261,
  title  = {Surfaces in a strict Walker 3-manifold that contain non-null curves with zero torsion},
  author = {El Hadji Baye Camara and Athoumane Niang and Ameth Ndiaye and Adama Thiandoum},
  journal= {arXiv preprint arXiv:2507.22261},
  year   = {2025}
}