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arXiv · 1805.09402

On a new class of infinitesimal group actions on pseudo-Riemannian manifolds

Sigbjørn Hervik
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Abstract

Using the Lie derivative of the metric we define a class of Lie algebras of vector fields by generalising the concept of Killing vectors. As a Lie algebra they define locally a group action on the pseudo-Riemannian manifold through exponentiation. The motivation behind studying these infinitesimal group actions is the investigation of $\mathcal{I}$-degenerate pseudo-Riemannian spaces, i.e., spaces having identical polynomial curvature invariants. In particular, we show that all the known examples of $\mathcal{I}$-degenerate pseudo-Riemannian spaces possess such vector fields.

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Sigbjørn Hervik. 2018-05-23. On a new class of infinitesimal group actions on pseudo-Riemannian manifolds. https://arxiv.org/abs/1805.09402

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