scholarly journals Nonexistence theorems for proper harmonic maps and harmonic morphisms between space forms of negative curvature

2004 ◽  
Vol 30 (2) ◽  
pp. 423-432
Author(s):  
Keisuke UENO
Keyword(s):  
Negative Curvature ◽  
Harmonic Maps ◽  
Harmonic Morphisms ◽  
Space Forms

Harmonic maps and harmonic morphisms

1999 ◽  
Vol 94 (2) ◽  
pp. 1263-1269 ◽  
Author(s):  
J. C. Wood
Keyword(s):  
Harmonic Maps ◽  
Harmonic Morphisms

Submetries of space-forms of negative curvature

1988 ◽  
Vol 28 (4) ◽  
pp. 552-562 ◽  
Author(s):  
V. N. Berestovskii
Keyword(s):  
Negative Curvature ◽  
Space Forms

scholarly journals Harmonic morphisms and conformal foliations by geodesics of three-dimensional space forms

1991 ◽  
Vol 51 (1) ◽  
pp. 118-153 ◽  
Author(s):  
Paul Baird ◽  
John C. Wood
Keyword(s):  
Space Form ◽  
Holomorphic Mapping ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Complete Classification ◽  
Harmonic Morphisms ◽  
Connected Space ◽  
Space Forms ◽  
Simply Connected ◽  
Three Dimensional Space

AbstractA complete classification is given of harmonic morphisms to a surface and conformal foliations by geodesics, with or without isolated singularities, of a simply-connected space form. The method is to associate to any such a holomorphic map from a Riemann surface into the space of geodesics of the space form. Properties such as nonintersecting fibres (or leaves) are translated into conditions on the holomorphic mapping which show it must have a simple form corresponding to a standard example.

Harmonic morphisms as a variational problem

1999 ◽  
Vol 129 (2) ◽  
pp. 385-393
Author(s):  
E. Loubeau
Keyword(s):  
Variational Problem ◽  
Harmonic Maps ◽  
Harmonic Morphisms

In this note, we establish a variational setting for harmonic morphisms for target spaces of any dimension. We then extend this result to horizontally weakly conformal p-harmonic maps, such maps being p-harmonic morphisms.

Harmonic Maps and Morphisms from Multilinear Norm-Preserving Mappings

1997 ◽  
Vol 08 (02) ◽  
pp. 187-211 ◽  
Author(s):  
Paul Baird ◽  
Ye-Lin Ou
Keyword(s):  
Harmonic Maps ◽  
Elliptic Functions ◽  
Hyperbolic Spaces ◽  
Harmonic Morphisms ◽  
Conformal Deformation ◽  
First Order ◽  
Independent Variables ◽  
Orthogonal Multiplication ◽  
Reduction Equation ◽  
Two Independent Variables

We extend the notion of orthogonal multiplication to multilinear norm-preserving mapping, using them to construct new eigenmaps into spheres. We characterize those which are harmonic morphisms. By the method of reduction we construct interesting families of harmonic morphisms into S2 from the product manifolds H2 × S3 and S3 × S3 of hyperbolic spaces and spheres. The corresponding reduction equation depends on two independent variables. We are able to solve the first-order horizontal conformality problem explicitly in terms of elliptic functions and then render the map harmonic by a conformal deformation of the metric.

scholarly journals Spectral geometry of harmonic maps into warped product manifolds II

2001 ◽  
Vol 27 (6) ◽  
pp. 327-339
Author(s):  
Gabjin Yun
Keyword(s):  
Riemannian Manifold ◽  
Warped Product ◽  
Space Form ◽  
Harmonic Maps ◽  
Harmonic Map ◽  
Jacobi Operator ◽  
Spectral Geometry ◽  
Product Manifold ◽  
Space Forms ◽  
Warped Product Manifold

Let(Mn,g)be a closed Riemannian manifold andNa warped product manifold of two space forms. We investigate geometric properties by the spectra of the Jacobi operator of a harmonic mapϕ:M→N. In particular, we show ifNis a warped product manifold of Euclidean space with a space form andϕ,ψ:M→Nare two projectively harmonic maps, then the energy ofϕandψare equal up to constant ifϕandψare isospectral. Besides, we recover and improve some results by Kang, Ki, and Pak (1997) and Urakawa (1989).

INFINITESIMAL DEFORMATIONS OF HARMONIC MAPS AND MORPHISMS

2006 ◽  
Vol 03 (05n06) ◽  
pp. 933-956 ◽  
Author(s):  
JOHN C. WOOD
Keyword(s):  
Harmonic Maps ◽  
Harmonic Morphisms ◽  
Laplace’S Equation ◽  
Jacobi Fields ◽  
Laplace's Equation ◽  
Infinitesimal Deformations ◽  
Survey Results

We survey results on infinitesimal deformations ("Jacobi fields") of harmonic maps, concentrating on (i) when they are integrable, i.e., arise from genuine deformations, and what this tells us, (ii) their relation with harmonic morphisms — maps which preserve Laplace's equation.

Sign in / Sign up

Export Citation Format

Share Document