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

Abstract

We propose a new method to construct degenerate $3$-$(\alpha ,\delta )$-Sasakian manifolds as fiber products of Boothby-Wang bundles over hyperkähler 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.

arXiv comment14 pages