Half-flat nilmanifolds

Abstract

We introduce a double complex that can be associated to certain Lie algebras, and show that its cohomology determines an obstruction to the existence of a half-flat SU(3)-structure. We obtain a classification of the 6-dimensional nilmanifolds carrying an invariant half-flat structure.

14 pages; v2: corrected equation in introduction; added solvable example; rearranged contents of Proposition 3 and Lemma 4; v3: corrected typos, added remark about unimodular case

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