INVESTIGADORES
BARBERIS Maria Laura Rita
artículos
Título:
NEW HKT MANIFOLDS ARISING FROM QUATERNIONIC REPRESENTATIONS
Autor/es:
M.L. BARBERIS, A. FINO
Revista:
MATHEMATISCHE ZEITSCHRIFT
Editorial:
SPRINGER
Referencias:
Lugar: Berlin / Heidelberg; Año: 2011 vol. 267 p. 717 - 735
ISSN:
0025-5874
Resumen:
We give a procedure for constructing an 8n-dimensional HKT Lie algebra starting from a 4n-dimensional one by using a quaternionic representation of the latter. The strong (respectively, weak, hyper-Kahler, balanced) condition is preserved by our construction. As an application of our results we obtain a new compact HKT manifold with holonomy in SL(n;H) which is not a nilmanifold. We nd in addition new compact strong HKT manifolds. We also show that every Kahler Lie algebra equipped with a at, torsion-free complex connection gives rise to an HKT Lie algebra. We apply this method to two distinguished 4-dimensional Kahler Lie algebras, thereby obtaining two conformally balanced HKT metrics in dimension 8. Both techniques prove to be an eective tool for giving the explicit expression of the corresponding HKT metrics.