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HYPERKÄHLER STRUCTURES WITH TORSION ON NILPOTENT LIE GROUPS

Published online by Cambridge University Press:  01 May 2003

BIRTE FEIX  and
HENRIK PEDERSEN
BIRTE FEIX
Affiliation:
Trinity Hall, Cambridge CB2 1TJ, England e-mail: B.Feix@dpmms.cam.ac.uk
HENRIK PEDERSEN
Affiliation:
Dept. of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark e-mail: henrik@imada.sdu.dk
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Abstract

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Using the classification by Dotti and Fino [3] we show the existence of an HKT metric on a neighbourhood of the centre of any 8-dimensional nilpotent Lie group $G$ with invariant hypercomplex structure. This metric exists globally if the hypercomplex structure is abelian, and in these cases we construct an HKT structure on a neighbourhood of the zero section of the cotangent bundle $T^{*}G$ extending the HKT metric on $G$.

Keywords

22E25
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 45 , Issue 1 , January 2003 , pp. 189 - 198
Copyright
2003 Glasgow Mathematical Journal Trust