English

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.

Keywords

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

R2 v1 2026-06-28T13:38:21.631Z