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arXiv · 2206.04002

On Degenerate $3$-$(\alpha,\delta)$-Sasakian Manifolds

Oliver Goertsches·Leon Roschig·Leander Stecker
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Abstract

We propose a new method to construct degenerate $3$-$(\alpha,\delta)$-Sasakian manifolds as fiber products of Boothby-Wang bundles over hyperk\"ahler manifolds. Subsequently, we study homogeneous degenerate $3$-$(\alpha, \delta)$-Sasakian manifolds and prove that no non-trivial compact examples exist as well as that there is exactly one family of nilpotent Lie groups with this geometry, the quaternionic Heisenberg groups.

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Oliver Goertsches, Leon Roschig, Leander Stecker. 2022-06-08. On Degenerate $3$-$(\alpha,\delta)$-Sasakian Manifolds. https://doi.org/10.1515/coma-2021-0142

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