Harmonic maps of bounded symmetric domains.
Harmonic maps of Lorentz surfaces, quadratic differentials and paraholomorphicity.
Harmonic maps of the hyperbolic space and development of singularities in wave maps and Yang-Mills fields
Harmonic Maps of the Moduli Space of Compact Riemann Surfaces.
Harmonic maps on contact metric manifolds
Harmonic maps on planar lattices
Harmonic maps on spaces with conical singularities
Harmonic maps which solve a free-boundary problem.
Harmonic morphisms and circle actions on 3- and 4-manifolds
Harmonic morphisms are considered as a natural generalization of the analytic functions of Riemann surface theory. It is shown that any closed analytic 3-manifold supporting a non-constant harmonic morphism into a Riemann surface must be a Seifert fibre space. Harmonic morphisms from a closed 4-manifold to a 3-manifold are studied. These determine a locally smooth circle action on with possible fixed points. This restricts the topology of . In all cases, a harmonic morphism from a closed...
Harmonic morphisms and non-linear potential theory
Originally, harmonic morphisms were defined as continuous mappings φ:X → X' between harmonic spaces such that h'∘φ remains harmonic whenever h' is harmonic, see [1], p. 20. In general linear axiomatic potential theory, one has to replace harmonic functions h' by hyperharmonic functions u' in this definition, in order to obtain an interesting class of mappings, see [3], Remark 2.3. The modified definition appears to be equivalent with the original one, provided X' is a Bauer space, i.e., a harmonic...
Harmonic morphisms and subharmonic functions.
Harmonic morphisms between semi-Riemannian manifolds.
Harmonic morphisms between Weyl spaces and twistorial maps II
We define, on smooth manifolds, the notions of almost twistorial structure and twistorial map, thus providing a unified framework for all known examples of twistor spaces. The condition of being a harmonic morphism naturally appears among the geometric properties of submersive twistorial maps between low-dimensional Weyl spaces endowed with a nonintegrable almost twistorial structure due to Eells and Salamon. This leads to the twistorial characterisation of harmonic morphisms between Weyl spaces...
Harmonic morphisms onto Riemann surfaces and generalized analytic functions
We study harmonic morphisms from domains in and to a Riemann surface , obtaining the classification of such in terms of holomorphic mappings from a covering space of into certain Grassmannians. We show that the only non-constant submersive harmonic morphism defined on the whole of to a Riemann surface is essentially the Hopf map.Comparison is made with the theory of analytic functions. In particular we consider multiple-valued harmonic morphisms defined on domains in and show how a cutting...
Harmonic sections and equivariant harmonic maps.
Harmonic symplectic spinors on Riemann surfaces.
Harmonic tori in spheres and complex projective spaces.
Harmonic -morphisms.
Harmonicity of horizontally conformal maps and spectrum of the Laplacian.
Harmonicity of vector fields on four-dimensional generalized symmetric spaces
Let (M = G/H;g)denote a four-dimensional pseudo-Riemannian generalized symmetric space and g = m + h the corresponding decomposition of the Lie algebra g of G. We completely determine the harmonicity properties of vector fields belonging to m. In some cases, all these vector fields are critical points for the energy functional restricted to vector fields. Vector fields defining harmonic maps are also classified, and the energy of these vector fields is explicitly calculated.