Complex product structures on 6-dimensional nilpotent Lie algebras

Details Complex product structures on 6-dimensional nilpotent Lie algebras Complex product structures on 6-dimensional nilpotent Lie algebras

2006-10-26

arxiv.org/abs/math/0610768v1

Mathematics

Differential Geometry

24 pages, to appear in Forum Math

Scientific paper

We study complex product structures on nilpotent Lie algebras, establishing some of their main properties, and then we restrict ourselves to 6 dimensions, obtaining the classification of 6-dimensional nilpotent Lie algebras admitting such structures. We prove that any complex structure which forms part of a complex product structure on a 6-dimensional nilpotent Lie algebra must be nilpotent in the sense of Cordero-Fern\'andez-Gray-Ugarte. A study is made of the torsion-free connection associated to the complex product structure and we consider also the associated hypercomplex structures on the 12-dimensional nilpotent Lie algebras obtained by complexification.

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