Complete biconservative surfaces in the hyperbolic space H3. (September 2020)

• Record Type: Journal Article
• Authors: Nistor, Simona; Oniciuc, Cezar
• Is Part Of: Nonlinear analysis. Volume 198(2020)
• Publication Date: 2020-09
• Subjects: 53A10 -- 53C40 -- 53C42; Biconservative surfaces -- Real space forms; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2020.111860
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We construct simply connected, complete, non- C M C biconservative surfaces in the 3-dimensional hyperbolic space H 3, 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 H 3 . 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 lying in a totally geodesic hyperbolic surface H 2 in H 3 .