Complex product structures on some simple Lie groups

Stefan Ivanov; Vasil Tsanov

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Complex product structures on some simple Lie groups

Stefan Ivanov·Vasil Tsanov

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Abstract

We construct invariant complex product (hyperparacomplex, indefinite quaternion) structures on the manifolds underlying the real noncompact simple Lie groups $SL(2m-1,\RR)$, $SU(m,m-1)$ and $SL(2m-1,\CC)^\RR$. We show that on the last two series of groups some of these structures are compatible with the biinvariant Killing metric. Thus we also provide a class of examples of compact (neutral) hyperparahermitean, non-flat Einstein manifolds.

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Stefan Ivanov, Vasil Tsanov. 2004-06-14. Complex product structures on some simple Lie groups. https://arxiv.org/abs/math/0405584

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