Generalized harmonic morphisms and horizontally weakly conformal biharmonic maps
نویسندگان
چکیده
منابع مشابه
Harmonic Maps and Biharmonic Maps
This is a survey on harmonic maps and biharmonic maps into (1) Riemannian manifolds of non-positive curvature, (2) compact Lie groups or (3) compact symmetric spaces, based mainly on my recent works on these topics.
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We give necessary and suucient conditions for a conformal foliation locally generated by conformal vector elds to produce harmonic morphisms. Natural constructions of harmonic maps and morphisms are thus obtained. Also we obtain reducibility results for harmonic morphisms induced by (innnitesimal) conformal actions on Einstein manifolds.
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We give a survey of harmonic morphisms between Riemannian manifolds, concentrating on their construction and relations with the geometry of foliations.
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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...
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Equivalences between conformal foliations on Euclidean 3-space, Hermitian structures on Euclidean 4-space, shear-free ray congruences on Minkowski 4-space, and holomorphic foliations on complex 4-space are explained geometrically and twistorially; these are used to show that 1) any real-analytic complex-valued harmonic morphism without critical points defined on an open subset of Minkowski spac...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2018
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2018.04.044