Morphisms between complete Riemannian pseudogroups
نویسندگان
چکیده
منابع مشابه
Harmonic Morphisms between Riemannian Manifolds
Harmonic morphisms are mappings between Riemannian manifolds which preserve Laplace’s equation. They can be characterized as harmonic maps which enjoy an extra property called horizontal weak conformality or semiconformality. We shall give a brief survey of the theory concentrating on (i) twistor methods, (ii) harmonic morphisms with one-dimensional fibres; in particular we shall outline the co...
متن کاملHarmonic Morphisms between Semi-riemannian Manifolds
A smooth map f: M ! N between semi-riemannian manifolds is called a harmonic morphism if f pulls back harmonic functions (i.e., local solutions of the Laplace{Beltrami equation) on N into harmonic functions on M. It is shown that a harmonic morphism is the same as a harmonic map which is moreover horizontally weakly conformal, these two notions being likewise carried over from the riemannian ca...
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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...
متن کاملHarmonic Morphisms between Riemannian Manifolds (london Mathematical Society Monographs: New Series 29)
spherical and hyperbolic space. It is divided into two equal-sized parts: the first is devoted to the two-dimensional case, where much more is known than in the n-dimensional setting, which is discussed in the second part. In addition, there is an appendix providing some important background information, essentially from convex geometry. Many of the sections end with interesting and stimulating...
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We enlarge the hom-sets of categories of complete lattices by introducing ‘state transitions’ as generalized morphisms. The obtained category will then be compared with a functorial quantaloidal enrichment and a contextual quantaloidal enrichment that uses a specific concretization in the category of sets and partially defined maps (Parset).
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2008
ISSN: 0166-8641
DOI: 10.1016/j.topol.2007.12.001