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arXiv · 2110.03603

Revisiting the Classification of Homogeneous 3-Sasakian and Quaternionic K\"ahler Manifolds

Oliver Goertsches·Leon Roschig·Leander Stecker
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Abstract

We provide a new, self-contained proof of the classification of homogeneous 3-Sasakian manifolds, which was originally obtained by Boyer, Galicki and Mann. In doing so, we construct an explicit one-to-one correspondence between simply connected homogeneous 3-Sasakian manifolds and simple complex Lie algebras via the theory of root systems. We also discuss why the real projective spaces are the only non-simply connected homogeneous 3-Sasakian manifolds and derive the famous classification of homogeneous positive quaternionic K\"ahler manifolds due to Wolf and Alekseevskii from our results.

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Oliver Goertsches, Leon Roschig, Leander Stecker. 2021-10-07. Revisiting the Classification of Homogeneous 3-Sasakian and Quaternionic K\"ahler Manifolds. https://arxiv.org/abs/2110.03603

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