View Full Version : Γενικό Σεμινάριο Πέμπτη 12-12-19

08-12-2019, 21:58
Ημερομηνία: Πέμπτη 12 Δεκεμβρίου 2019
Ώρα: 13:00-14:00
Ομιλητής: Professor Sigmundur Gudmundsson (Lund University, Sweden)
Τίτλος: Complex-Valued Harmonic Morphisms from Lie Groups and Symmetric Spaces
Αίθουσα: 342 (Βιολογίας/Μαθηματικού)

Περίληψη: The study of harmonic morphisms in the 3-dimensional Euclidean space goes back to a paper of Jacobi from 1848. This was then introduced into the setting of Riemannian geometry, in the late 1970s by Fuglede and Ishihara, independently. A harmonic morphism $\phi:(M,g)\to (N,h)$ between two Riemannian manifolds is a map that pulls back real-value harmonic functions on $(N,h)$ to harmonic functions on $(M,g)$. In 1983 Baird and Eells have shown that in the case when the codomain is a surface, the regular fibres of a harmonic morphism form a minimal conformal foliation on the domain. These are interesting geometric objects and our main motivation for studying harmonic morphisms in this particular case. Harmonic morphisms are solutions to an over-determined non-linear system of partial differential equations. They do not have a general existence theory. There even exist rather simple 3-dimensional Lie groups for which one can show that local solutions do not exist. In this talk we will explain the general theory and give a survey of what is known when $(M, g)$ is a Lie group or a symmetric space and $(N, h)$ is the flat complex plane.