A class of Sasakian 5-manifolds

Details A class of Sasakian 5-manifolds A class of Sasakian 5-manifolds

2008-07-11

arxiv.org/abs/0807.1800v2

Mathematics

Differential Geometry

The title has been shortened; references added or updated; typos corrected. Formula (4) corrected. Some changes in the introdu

Scientific paper

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 $\R \ltimes (H_3 \times \R)$. In particular, the compact quotient is an $S^1$-bundle over a 4-dimensional K\"ahler solvmanifold.

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