Harmonic Morphisms on Heaven Spaces
نویسنده
چکیده
We prove that any (real or complex) analytic horizontally conformal submersion from a three-dimensional conformal manifold (M, cM ) to a twodimensional conformal manifold (N, cN ) can be, locally, ‘extended’ to a unique harmonic morphism from the H(eaven)-space (H, g) of (M, cN ) to (N, cN ). Moreover, any positive harmonic morphism with two-dimensional fibres from (H, g) is obtained this way.
منابع مشابه
On the Classification of Quadratic Harmonic Morphisms between Euclidean Spaces
We give a classification of quadratic harmonic morphisms between Euclidean spaces (Theorem 2.4) after proving a Rank Lemma. We also find a correspondence between umbilical (Definition 2.7) quadratic harmonic morphisms and Clifford systems. In the case R −→ R, we determine all quadratic harmonic morphisms and show that, up to a constant factor, they are all bi-equivalent (Definition 3.2) to the ...
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