Mathematics, Faculty of ScienceSigmundur GudmundssonResearch Interests |
His recent work is mainly devoted to the existence theory of complex-valued harmonic morphisms from Riemannian homogeneous spaces of various types, such as symmetric spaces and semisimple, solvable and nilpotent Lie groups.
Lecture Notes: Harmonic Morphisms - Basics -
Lecture Notes: Harmonic Morphisms - Some Existence Theory -
Harmonic maps are very important both in classical and modern differential geometry. The best known application is their parametrization of both geodesics and minimal surfaces in Riemannian manifolds. Other important examples are the holomorphic maps between any two Kähler manifolds, generalizing the classical holomorphic maps between complex vector spaces.
For further information on harmonic maps interested readers should check the following sources:
Here you'll find HM^{2}I-2000, Workshop on Harmonic Maps and Minimal Immersions, Caparide (Lisbon), Portugal · February 1-5, 2000
Here you'll find Differential Geometry Workshop, Harmonic maps, biharmonic maps, harmonic morphisms and related topics, Cagliari/Italy · 10 - 12 June 2015
The case when the manifold N is a surface, i.e. 2-dimensional, is of particular interest. Then harmonic morphisms (M,g) --> (N^2,h) have many nice geometric properties. Every regular fibre of such a map is a minimal submanifold of (M,g) of codimension 2. This means that harmonic morphisms are useful tools for the construction of such submanifolds. Interesting examples are holomorphic maps from Kähler manifolds to Riemann surfaces.
Most of my recent work is devoted to the existence theory of complex-valued harmonic morphisms from Riemannian homogeneous spaces of various types, such as symmetric spaces and semisimple, solvable and nilpotent Lie groups.
Here you'll find a comprehensive list of articles on harmonic morphisms.
Here you'll find THE ATLAS OF HARMONIC MORPHISMS, a guide to the theory of harmonic morphisms.
Here you'll find a Bibliography on foliations.
The first international conference primarily devoted to harmonic morphisms was held 7 July - 11 July 1997 at the Université de Bretagne Occidentale, Brest, France.
The second international conference primarily devoted to harmonic morphisms was held at the Centre International de Rencontres Mathématiques in Luminy, France from 28 May to 1 June 2001. Here is a PHOTOGRAPH of the participants.