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Harmonic morphisms, complex analysis and how to generalize it

Sigmundur Gudmundsson
(Lund University)
Onsdag, 14 marts, 2012, at 14:15-15:15, in Aud. G1 (1532-116)
It is a well-known result in classical complex analysis that every holomorphic or anti-holomorphic function is harmonic and conformal. It is easy to see that they also pull back harmonic real-valued functions to harmonic functions. This last property actually characterizes the holomorphic and anti- holomorphic functions in the complex plane. Harmonic morphisms are maps (M,g) -> (N,h) between Riemannian manifolds which pull back harmonic functions to harmonic functions. They have many properties similar to those of holomorphic functions which they generalize. We will give a general introduction to the theory of harmonic morphisms.
Kontaktperson: Andrew Swann