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

2025/07/29 by El Hadji Baye Camara, Athoumane Niang, Camara, El Hadji Baye +5
Mathematics · #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2507.22261

openalex publication_date 2025/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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