On the existence of complex-valued harmonic morphisms

Jonas Nordström

Research output: ThesisDoctoral Thesis (compilation)

174 Downloads (Pure)

Abstract

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 $G_{2}$ 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.
Original languageEnglish
QualificationDoctor
Awarding Institution
  • Mathematics (Faculty of Sciences)
Supervisors/Advisors
  • Gudmundsson, Sigmundur, Supervisor
Award date2015 Sept 9
Publisher
ISBN (Print)978-91-7623-291-0
Publication statusPublished - 2015

Bibliographical note

Defence details

Date: 2015-09-09
Time: 13:00
Place: Sölvegatan 18, Lund, sal MH:C

External reviewer(s)

Name: Montaldo, Stefano
Title: Dr.
Affiliation: University of Cagliari

---

Subject classification (UKÄ)

  • Mathematics

Free keywords

  • Harmonic morphisms
  • foliations
  • minimal submanifolds
  • Lie groups

Fingerprint

Dive into the research topics of 'On the existence of complex-valued harmonic morphisms'. Together they form a unique fingerprint.

Cite this