2019/09/27 by Simona Nistor, Nistor, Simona, Cezar Oniciuc +1
Mathematics · #53A10 (Primary) #53C40 #53C42 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1909.12709
openalex publication_date 2019/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct simply connected, complete, non-CMC biconservative surfaces in the 3-dimensional hyperbolic space ℍ3 in an intrinsic and extrinsic way. We obtain three families of such surfaces, and, for each surface, the set of points where the gradient of the mean curvature function does not vanish is dense and has two connected components. In the intrinsic approach, we first construct a simply connected, complete abstract surface and then prove that it admits a unique biconservative immersion in ℍ3. Working extrinsically, we use the images of the explicit parametric equations and a gluing process to obtain our surfaces. They are made up of circles (or hyperbolas, or parabolas, respectively) which lie in 2-affine parallel planes and touch a certain curve in a totally geodesic hyperbolic surface ℍ2 in ℍ3.