Open Access
April 2014 SU(3)-holonomy metrics from nilpotent Lie groups
Diego Conti
Asian J. Math. 18(2): 281-320 (April 2014).


One way of producing explicit Riemannian 6-manifolds with holonomy SU(3) is by integrating a flow of SU(2)-structures on a 5-manifold, called the hypo evolution flow. In this paper we classify invariant hypo SU(2)-structures on nilpotent 5-dimensional Lie groups. We characterize the hypo evolution flow in terms of gauge transformations, and study the flow induced on the variety of frames on a Lie algebra taken up to automorphisms. We classify the orbits of this flow for all hypo nilpotent structures, obtaining several families of cohomogeneity one metrics with holonomy contained in SU(3). We prove that these metrics cannot be extended to a complete metric, unless they are flat.


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Diego Conti. "SU(3)-holonomy metrics from nilpotent Lie groups." Asian J. Math. 18 (2) 281 - 320, April 2014.


Published: April 2014
First available in Project Euclid: 27 August 2014

zbMATH: 1307.14022
MathSciNet: MR3217638

Primary: 53C25
Secondary: 17B30 , 53C29 , 53C42

Keywords: cohomogeneity one , nilmanifold , SU(3) holonomy

Rights: Copyright © 2014 International Press of Boston

Vol.18 • No. 2 • April 2014
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