Work

The completeness problem on the pseudo-homothetic Lie group

Year: 2025

Type: article

Abstract: Let us call pseudo-homothetic group the non-unimodular 3-dimensional Lie group that is the semi-direct product of R acting non-semisimply on R 2 . In this article, we solve the geodesic completeness problem on this Lie group. In particular, we exhibit a family of complete metrics such that all geodesics have bounded velocity. As an application, we show that the set of complete metrics is not closed.

Source: Differential Geometry and its Applications

DOI: 10.1016/j.difgeo.2025.102288

Authors: Salah Chaib, Ana Cristina Ferreira, Abdelghani Zeghib

Institutions: Centro de Matemática, University of Minho, École Normale Supérieure de Lyon, Centre National de la Recherche Scientifique, Unité de Mathématiques Pures et Appliquées

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,740