Harmonic maps on contact metric manifolds
Harmonic maps on spaces with conical singularities
Harmonic maps which solve a free-boundary problem.
Harmonic metrics on four dimensional non-reductive homogeneous manifolds
We study harmonic metrics with respect to the class of invariant metrics on non-reductive homogeneous four dimensional manifolds. In particular, we consider harmonic lifted metrics with respect to the Sasaki lifts, horizontal lifts and complete lifts of the metrics under study.
Harmonic morphisms between degenerate semi-Riemannian manifolds.
Harmonic morphisms between riemannian manifolds
A harmonic morphism between Riemannian manifolds and is by definition a continuous mappings which pulls back harmonic functions. It is assumed that dim dim, since otherwise every harmonic morphism is constant. It is shown that a harmonic morphism is the same as a harmonic mapping in the sense of Eells and Sampson with the further property of being semiconformal, that is, a conformal submersion of the points where vanishes. Every non-constant harmonic morphism is shown to be an open mapping....
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 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.
Harmonie Forms Dual to Geodesic Cycles in Quotients of SU (p, 1).
Harmonie Mappings and Kähler Manifolds.
Harmonie reflections
We study local reflections with respect to a curve in a Riemannian manifold and prove that is a geodesic if is a harmonic map. Moreover, we prove that the Riemannian manifold has constant curvature if and only if is harmonic for all geodesies .
Harnack inequalities for curvature flows depending on mean curvature.
Harnack inequalities for evolving hypersurfaces.
Hausdorff convergence and the fundamental group.
Hausdorff dimensions of limit sets I.