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Conformal holonomy of bi-invariant metrics

Felipe Leitner
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Abstract

We discuss in this paper the conformal geometry of bi-invariant metrics on compact semisimple Lie groups. For this purpose we develop a conformal Cartan calculus adapted to this problem. In particular, we derive an explicit formula for the holonomy algebra of the normal conformal Cartan connection of a bi-invariant metric. As an example, we apply this calculus to the group $\SO(4)$. Its conformal holonomy group is calculated to be $\SO(7)$.

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Felipe Leitner. 2004-06-15. Conformal holonomy of bi-invariant metrics. https://arxiv.org/abs/math/0406299

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