2026-10-09T21:06:35Z https://lup.lub.lu.se/oai

oai:lup.lub.lu.se:537bfff7-efcd-47cc-9e9f-94ab8f7f169a 2026-02-03T06:51:23Z allFtxt allFtxt thesis thesis:ftxt thesis:doccomp thesis:doccomp:ftxt

On the existence of complex-valued harmonic morphisms https://lup.lub.lu.se/record/5425323 urn:isbn:978-91-7623-291-0 https://portal.research.lu.se/files/3846241/5425587.pdf Nordström, Jonas 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. Mathematical Sciences Harmonic morphisms foliations minimal submanifolds Lie groups eng Doctoral Theses in Mathematical Sciences; 2015:5 (2015) ISSN: 1404-0034 Centre for Mathematical Sciences, Lund University 2015 info:eu-repo/semantics/openAccess thesis/doccomp info:eu-repo/semantics/doctoralThesis text application/pdf