Pseudo-parallel Lorentzian Surfaces in Pseudo-Riemannian Space Forms

Author(s)

Lobos, Guillermo ; Melara, Mynor ; Palmas, Oscar

• Document type: Journal article
• Source: Results in Mathematics; v. 78, n. 2, p. 30-pg., 2023-04-01.

Abstract

In this work, we give a characterization of pseudo-parallel Lorentzian surfaces with non-flat normal bundle in pseudo-Riemannian space forms as lambda\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\uplambda $$\end{document}-isotropic surfaces, extending an analogous result by Asperti-Lobos-Mercuri for the pseudo-parallel case in Riemannian space forms. In addition, for this kind of pseudo-parallel surfaces we give a characterization using the concept of hyperbola of curvature. In particular, we get a non-existence result for pseudo-parallel Lorentzian surfaces with non-flat normal bundle in Lorentzian space forms. Moreover, in codimension two, we show that locally any pseudo-parallel Lorentzian surface with non-flat normal bundle and constant pseudo-parallelism function is congruent to a piece of a Lorentzian surface of the Veronese type. Finally, an example of an extremal and flat pseudo-parallel Lorentzian surface with non-flat normal bundle which is not a semi-parallel surface is given in codimension three. (AU)

• FAPESP's process: 16/23746-6 - Algebraic, topological and analytical techniques in differential geometry and geometric analysis
• Grantee: Paolo Piccione
• Support Opportunities: Research Projects - Thematic Grants