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Torsion-free G*2(2)-structures with full holonomy on nilmanifolds
-
Anna Fino
and
Ignacio Luján
Published/Copyright:
July 3, 2015
Abstract
We study the existence of invariant metrics with holonomy G* 2(2) ⊂ SO(4, 3) on compact nilmanifolds, i.e. on compact quotients of nilpotent Lie groups by discrete subgroups. We prove that, up to isomorphism, there exists only one indecomposable nilpotent Lie algebra admitting a torsion-free G* 2(2)-structure such that the center is definite with respect to the induced inner product. In particular, we show that the associated compact nilmanifold admits a 3-parameter family of invariant metrics with full holonomy G* 2(2).
Received: 2013-11-18
Revised: 2014-3-11
Published Online: 2015-7-3
Published in Print: 2015-7-1
© 2015 by Walter de Gruyter Berlin/Boston
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- A natural extension of the Young partition lattice
- Pencils of small degree on curves on unnodal Enriques surfaces
- Michael’s Selection Theorem in a semilinear context
- Quasi-simple Lie groups as multiplication groups of topological loops
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Articles in the same Issue
- Frontmatter
- A natural extension of the Young partition lattice
- Pencils of small degree on curves on unnodal Enriques surfaces
- Michael’s Selection Theorem in a semilinear context
- Quasi-simple Lie groups as multiplication groups of topological loops
- Some spectral results on Kakeya sets
- Projective normality and the generation of the ideal of an Enriques surface
- Topological contact dynamics I: symplectization and applications of the energy-capacity inequality
- Torsion-free G*2(2)-structures with full holonomy on nilmanifolds
