INVESTIGADORES
BARBERIS Maria Laura Rita
artículos
Título:
Canonical bundles of complex nilmanifolds, with applications to hypercomplex geometry
Autor/es:
M.L. BARBERIS, I.G. DOTTI, M. VERBITSKY
Revista:
MATHEMATICAL RESEARCH LETTERS
Editorial:
International Press
Referencias:
Lugar: San Diego; Año: 2009 vol. 16 p. 331 - 347
ISSN:
1073-2780
Resumen:
A nilmanifold is a quotient of a nilpotent group $G$ by a co-compactdiscrete subgroup. A complex nilmanifold is one which is equippedwith a $G$-invariant complex structure. We prove that a complexnilmanifold has trivial canonical bundle. This is used to studyhypercomplex nilmanifolds (nilmanifolds with a triple of$G$-invariant complex structures which satisfy quaternionicrelations). We prove that a hypercomplex nilmanifold admits an HKT(hyperk"ahler with torsion) metric if and only if the underlyinghypercomplex structure is abelian. Moreover, any $G$-invariantHKT-metric on a nilmanifold is balanced with respect to allassociated complex structures.
