Harmonic morphisms from 5-dimensional Lie groups

We consider 5-dimensional Lie groups equipped with a left-invariant Riemannian metric. On such groups we construct left-invariant conformal foliations with minimal leaves of codimension 2. These foliations produce complex-valued harmonic morphisms locally defined on the Lie group.

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Bibliographic Details
Published in:	Geometriae dedicata Vol. 184; no. 1; pp. 143 - 157
Main Author:	Gudmundsson, Sigmundur
Format:	Journal Article
Language:	English
Published:	Dordrecht Springer Netherlands 01-10-2016 Springer Nature B.V
Subjects:	Algebraic Geometry Convex and Discrete Geometry Differential Geometry Hyperbolic Geometry Invariants Lie groups Mathematics Mathematics and Statistics Original Paper Projective Geometry Topology Harmonic morphisms 58E20 53C12 Minimal submanifolds Lie groups 53C43
Online Access:	Get full text
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Description
Summary:	We consider 5-dimensional Lie groups equipped with a left-invariant Riemannian metric. On such groups we construct left-invariant conformal foliations with minimal leaves of codimension 2. These foliations produce complex-valued harmonic morphisms locally defined on the Lie group.
ISSN:	0046-5755 1572-9168
DOI:	10.1007/s10711-016-0162-4