منابع مشابه
The Geometry of Harmonic Maps and Morphisms
We give a survey of harmonic morphisms between Riemannian manifolds, concentrating on their construction and relations with the geometry of foliations.
متن کاملInfinitesimal Deformations of Harmonic Maps and Morphisms
Harmonic maps are mappings between Riemannian manifolds which extremize a natural energy functional. They have been studied for many years in differential geometry, and in particle physics as nonlinear sigma models. We shall report on recent progress in understanding their infinitesimal deformations, the so-called Jacobi fields. It is important to know whether the Jacobi fields along harmonic m...
متن کاملClassifications of some special infinity-harmonic maps
∞-Harmonic maps are a generalization of ∞-harmonic functions. They can be viewed as the limiting cases of p-harmonic maps as p goes to infinity. In this paper, we give complete classifications of linear and quadratic ∞-harmonic maps from and into a sphere, quadratic ∞-harmonic maps between Euclidean spaces. We describe all linear and quadratic ∞-harmonic maps between Nil and Euclidean spaces, b...
متن کاملComplete 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...
متن کاملIsometric Actions and Harmonic Morphisms
We give the necessary and suucient condition for a Riemannian foliation, of arbitrary dimension, locally generated by Killing elds to produce harmonic morphisms. Natural constructions of harmonic maps and morphisms are thus obtained.
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ژورنال
عنوان ژورنال: Differential Geometry and its Applications
سال: 2012
ISSN: 0926-2245
DOI: 10.1016/j.difgeo.2011.11.011