Conformal holonomy of bi-invariant metrics

Felipe Leitner

Conformal holonomy of bi-invariant metrics

Differential Geometry 2007-05-23 v1

Authors: Felipe Leitner

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 $\SO(7)$ .

Keywords

bi-invariant metric conformal geometry cartan calculus holonomy algebra semisimple lie group conformal holonomy

Cite

@article{arxiv.math/0406299,
  title  = {Conformal holonomy of bi-invariant metrics},
  author = {Felipe Leitner},
  journal= {arXiv preprint arXiv:math/0406299},
  year   = {2007}
}

Comments

14 pages

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