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arXiv · 2312.00569

Killing vector fields on semi-Riemannian product manifolds

Federico Costanza·Thomas Leistner
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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.

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Federico Costanza, Thomas Leistner. 2023-12-01. Killing vector fields on semi-Riemannian product manifolds. https://arxiv.org/abs/2312.00569

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