3-dimensional Levi-Civita metrics with projective vector fields

3-dimensional Levi-Civita metrics with projective vector fields

Volume 163, July 2022, Pages 473-517 Projective vector fields are the infinitesimal transformations whose local flow preserves geodesics up to reparametrisation. In 1882 Sophus Lie posed the problem of describing 2-dimensional metrics admitting a non-trivial projective vector field, which was solved...

Full description

Saved in:
Bibliographic Details
Main Authors: Manno, Gianni, Vollmer, Andreas
Format: Journal Article
Language:English
Published: 02-12-2021
Subjects:
Mathematics - Differential Geometry
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Volume 163, July 2022, Pages 473-517 Projective vector fields are the infinitesimal transformations whose local flow preserves geodesics up to reparametrisation. In 1882 Sophus Lie posed the problem of describing 2-dimensional metrics admitting a non-trivial projective vector field, which was solved in recent years. In the present paper, we solve the analog of Lie's problem in dimension 3, for Riemannian metrics and, more generally, for Levi-Civita metrics of arbitrary signature.
DOI:10.48550/arxiv.2110.06785