{"id":{"repo_id":"lund","oai_identifier":"oai:lup.lub.lu.se:537bfff7-efcd-47cc-9e9f-94ab8f7f169a"},"canonical_url":"https://search.dev.ndltd.org/etd/lund/oai:lup.lub.lu.se:537bfff7-efcd-47cc-9e9f-94ab8f7f169a","repository":{"repo_id":"lund","name":"University of Lund","base_url":"https://lup.lub.lu.se/oai"},"display":{"title":"On the existence of complex-valued harmonic morphisms","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.","abstract_html":"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 <span class=\"etd-inline-math\">G<sub>2</sub></span> 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.","abstract_has_math":true,"creators":["Nordström, Jonas"],"institution":"Centre for Mathematical Sciences, Lund University","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015","date_published":"2015","updated_at":"2026-07-24T02:59:49Z","subjects":["Mathematical Sciences","Harmonic morphisms","foliations","minimal submanifolds","Lie groups"],"languages":["eng"],"rights":["info:eu-repo/semantics/openAccess"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["urn:isbn:978-91-7623-291-0"],"render_values":[{"text":"urn:isbn:978-91-7623-291-0","href":null,"code":true}]}]},"links":{"outbound_url":"https://lup.lub.lu.se/record/5425323","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Nordström, Jonas"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015"]},{"key":"dc:publisher","label":"Institution","values":["Centre for Mathematical Sciences, Lund University"]},{"key":"dc:type","label":"Dc Type","values":["thesis/doccomp","info:eu-repo/semantics/doctoralThesis","text"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematical Sciences","Harmonic morphisms","foliations","minimal submanifolds","Lie groups"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["info:eu-repo/semantics/openAccess"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://lup.lub.lu.se/record/5425323","urn:isbn:978-91-7623-291-0","https://portal.research.lu.se/files/3846241/5425587.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:source","label":"Dc Source","values":["Doctoral Theses in Mathematical Sciences; 2015:5 (2015)","ISSN: 1404-0034"]},{"key":"dc:title","label":"Title","values":["On the existence of complex-valued harmonic morphisms"]}]}],"canonical_facts":{"dc:creator":["Nordström, Jonas"],"dc:date":["2015"],"dc:description":["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."],"dc:format":["application/pdf"],"dc:identifier":["https://lup.lub.lu.se/record/5425323","urn:isbn:978-91-7623-291-0","https://portal.research.lu.se/files/3846241/5425587.pdf"],"dc:language":["eng"],"dc:publisher":["Centre for Mathematical Sciences, Lund University"],"dc:rights":["info:eu-repo/semantics/openAccess"],"dc:source":["Doctoral Theses in Mathematical Sciences; 2015:5 (2015)","ISSN: 1404-0034"],"dc:subject":["Mathematical Sciences","Harmonic morphisms","foliations","minimal submanifolds","Lie groups"],"dc:title":["On the existence of complex-valued harmonic morphisms"],"dc:type":["thesis/doccomp","info:eu-repo/semantics/doctoralThesis","text"]},"updated_at":"2026-07-24T02:59:49Z"}