A class of Sasakian 5-manifolds

ADRIÁN ANDRADA; ANNA FINO; LUIGI VEZZONI

TRANSFORMATION GROUPS

Birkhäuser

Lugar: Boston; Año: 2009 vol. 14 p. 493 - 512

1083-4362

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 H_{2n+1}. Furthermore, we classify Sasakian Lie algebras of dimension 5 and determine which of them carry a Sasakian alpha-Einstein structure. We show that a 5-dimensional solvable Lie group with a left-invariant Sasakian structure and which admits a compact quotient by a discrete subgroup is isomorphic to either H_5 or a semidirect product $R ltimes (H_3 x R)$. In particular, the compact quotient is an S^1-bundle over a 4-dimensional Kähler solvmanifold.