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.
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 language | English |
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Qualification | Doctor |
Awarding Institution |
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Supervisors/Advisors |
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Award date | 2015 Sept 9 |
Publisher | |
ISBN (Print) | 978-91-7623-291-0 |
Publication status | Published - 2015 |
Bibliographical note
Defence detailsDate: 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
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Subject classification (UKÄ)
- Mathematics
Free keywords
- Harmonic morphisms
- foliations
- minimal submanifolds
- Lie groups