On the existence of complex-valued harmonic morphisms

This thesis consists of 4 papers, their content is described below: Paper I. We present a new method for manufacturing complex-valued harmonic morphisms from a wide class of Riemannian Lie groups. This yields new solutions from an important family of homogeneous Hadamard manifolds. We also give a new method for constructing left-invariant foliations on a large class of Lie groups producing harmonic morphisms. Paper II. We study left-invariant complex-valued harmonic morphisms from Riemannian Lie groups. We show that in each dimension greater than $3$ there exist Riemannian Lie groups that do not have any such solutions. Paper III. We construct harmonic morphisms on the compact simple Lie group G₂ using eigenfamilies. The construction of eigenfamilies uses a representation theory scheme and the seven-dimensional cross product. Paper IV. We study the curvature of a manifold on which there can be defined a complex-valued submersive harmonic morphism with either, totally geodesic fibers or that is holomorphic with respect to a complex structure which is compatible with the second fundamental form. We also give a necessary curvature condition for the existence of complex-valued harmonic morphisms with totally geodesic fibers on Einstein manifolds.

Grantor dc:publisher

Centre for Mathematical Sciences, Lund University

Year dc:date

2015

Author dc:creator

• Nordström, Jonas

• Mathematical Sciences
• Harmonic morphisms
• foliations
• minimal submanifolds
• Lie groups

Statement dc:rights

• info:eu-repo/semantics/openAccess

Language dc:language

eng

Identifier

urn:isbn:978-91-7623-291-0

OAI identifier oai:identifier

oai:lup.lub.lu.se:537bfff7-efcd-47cc-9e9f-94ab8f7f169a