fLk-Harmonic Maps and fLk-Harmonic Morphisms

2020 ◽  
Author(s):  
Mehran Aminian ◽  
Mehran Namjoo
Keyword(s):  
Harmonic Maps ◽  
Harmonic Morphisms

Harmonic maps and harmonic morphisms

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

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.

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.

scholarly journals Harmonic Maps on Kenmotsu Manifolds

2013 ◽  
Vol 21 (3) ◽  
pp. 197-208
Author(s):  
Najma Abdul Rehman
Keyword(s):  
Spectral Theory ◽  
Harmonic Maps ◽  
Harmonic Map ◽  
Harmonic Morphisms ◽  
Kenmotsu Manifold ◽  
Kenmotsu Manifolds ◽  
Target Manifold

AbstractWe study in this paper harmonic maps and harmonic morphisms on Kenmotsu manifolds. We also give some results on the spectral theory of a harmonic map for which the target manifold is a Kenmotsu manifold.

scholarly journals Pseudo Harmonic Morphisms

1997 ◽  
Vol 08 (07) ◽  
pp. 943-957 ◽  
Author(s):  
E. Loubeau
Keyword(s):  
Harmonic Maps ◽  
Harmonic Morphisms ◽  
Geometrical Condition

We study a geometrical condition (PHWC) which is weaker than horizontal weak conformality. In particular, we show that harmonic maps satisfying this condition, which will be called pseudo harmonic morphisms, include harmonic morphisms and can be described as pulling back certain germs to certain other germs. Finally, we construct a canonical f-structure associated to every map satisfying (PHWC) and find conditions on this f-structure to ensure the harmonicity of the map.

Sign in / Sign up

Export Citation Format

Share Document