C:/Documents and Settings/Jonas/Mina dokument/Matematik master/Rapport/master-jonasn.dvi
نویسنده
چکیده
In this thesis we investigate the existence of complex-valued harmonic morphisms on Lie groups and homogeneous Hadamard manifolds. The Lie groups that we are interested in have a particular decomposition of their Lie algebra. This decomposition allows us to define harmonic morphisms to R, n ≥ 2. Any homogeneous Hadamard manifold is isometric to a solvable Lie group S with a left-invariant metric. We give sufficient conditions for the Lie algebra of S to have a decomposition that allows us to define complex-valued harmonic morphisms.
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C:/Documents and Settings/Jonas/Mina dokument/Exjobb/Tex/X-jobb-jonasn.dvi
In the 1960s E. Calabi classified all minimal isometric immersions, from the 2sphere into higher dimensional spheres S, in terms of holomorphic maps. He showed that such a map can be lifted to a horizontal holomorphic map from S ∼= CP 1 into a twistor space over S. The construction also applies to harmonic maps from S to S. The main purpose of this work is to give a detailed presentation of Cal...
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