On Degenerate 3-(α, δ)-Sasakian Manifolds

Abstract

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

Keywords

• sasakian geometry
• hyperkähler manifolds
• homogeneous spaces
• boothby-wang bundle
• nilpotent lie groups
• quaternionic heisenberg groups
• 53c25
• 53c26
• 53c30
• 22e25