The completeness problem on the pseudo-homothetic Lie group

IF 0.7 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications Pub Date : 2025-09-09 DOI:10.1016/j.difgeo.2025.102288

Salah Chaib , Ana Cristina Ferreira , Abdelghani Zeghib

引用次数: 0

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.

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伪齐调李群上的完备性问题

我们称伪同群为非单模的三维李群，它是R作用于R2上的非半单模的半直积。本文解决了该李群上的测地线完备性问题。特别地，我们展示了一组完备的度量，使得所有测地线的速度都有界。作为一个应用程序，我们展示了完整度量的集合不是封闭的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Differential Geometry and its Applications 数学-数学

CiteScore

1.00

自引率

20.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.