Killing vector fields on semi-Riemannian product manifolds
Differential Geometry
2023-12-04 v1
Abstract
Hano's theorem states that the space of Killing vector fields of a complete simply connected Riemannian manifold is isomorphic to the direct sum of the Killing vector fields of the factors in its de Rham decomposition. We prove a generalisation of this theorem to manifolds with indefinite metrics that requires an assumption on the factors, and show by example why this assumption is needed.
Cite
@article{arxiv.2312.00569,
title = {Killing vector fields on semi-Riemannian product manifolds},
author = {Federico Costanza and Thomas Leistner},
journal= {arXiv preprint arXiv:2312.00569},
year = {2023}
}
Comments
Dedicated to the Memory of Joseph A. Wolf