Caloric morphisms with respect to radial metrics on semi-euclidean spaces

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 ...

Complete Lifts of Harmonic Maps and Morphisms between Euclidean Spaces

We introduce the complete lifts of maps between (real and complex) Euclidean spaces and study their properties concerning holomorphicity, harmonicity and horizontal weakly conformality. As applications, we are able to use this concept to characterize holomorphic maps φ : C ⊃ U −→ C (Proposition 2.3) and to construct many new examples of harmonic morphisms (Theorem 3.3). Finally we show that the...

More on Morphisms of Spaces

Harmonic Morphisms on Heaven Spaces

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.

Spatial Analysis in curved spaces with Non-Euclidean Geometry

The ultimate goal of spatial information, both as part of technology and as science, is to answer questions and issues related to space, place, and location. Therefore, geometry is widely used for description, storage, and analysis. Undoubtedly, one of the most essential features of spatial information is geometric features, and one of the most obvious types of analysis is the geometric type an...