A class of Sasakian 5-manifolds

By Adrián Andrada, Anna Fino, Luigi Vezzoni. 2008

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We obtain some general results on Sasakian Lie algebras and prove as a consequence that a (2n + 1)-dimensional nilpotent Lie group admitting left-invariant Sasakian structures is isomorphic to the real Heisenberg group H2n + 1. Furthermore, we classify Sasakian Lie algebras of dimension five and determine which of them carries a Sasakian α-Einstein structure. We show that a five-dimensional solvable Lie group with a left-invariant Sasakian structure and which admits a compact quotient by a discrete subgroup is isomorphic to either H5 or a semidirect product ℝ ⋉ (H3 × ℝ). In particular, the compact quotient is an S1-bundle over a four-dimensional Kähler solvmanifold.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/efd6b1e993d55afa62d295a1e4d414ff8daa3524