Asian Journal of Mathematics

Volume 18 (2014)

Number 2

Non-nilpotent complex geometry of nilmanifolds and heterotic supersymmetry

Pages: 229 – 246



Luis Ugarte (Departamento de Matemáticas, Universidad de Zaragoza, Spain)

Raquel Villacampa (Centro Universitario de la Defensa, Academia General Militar, Zaragoza, Spain)


We classify non-nilpotent complex structures on 6-nilmanifolds and their associated invariant balanced metrics. As an application we find a large family of solutions of the heterotic supersymmetry equations with non-zero flux, non-flat instanton and constant dilaton satisfying the anomaly cancellation condition with respect to the Chern connection.


complex structure, Chern connection, balanced Hermitian metric, Strominger system

2010 Mathematics Subject Classification

53C29, 53C55, 81T30

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