scholarly journals Generalized harmonic morphisms and horizontally weakly conformal biharmonic maps

2018 ◽  
Vol 464 (1) ◽  
pp. 924-938 ◽  
Author(s):  
Elsa Ghandour ◽  
Ye-Lin Ou
Keyword(s):  
Harmonic Morphisms ◽  
Biharmonic Maps

Harmonic maps and harmonic morphisms

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

On holomorphic harmonic morphisms

2002 ◽  
Vol 107 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Martin Svensson
Keyword(s):  
Harmonic Morphisms

scholarly journals Harmonic Morphisms Projecting Harmonic Functions to Harmonic Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-8
Author(s):  
M. T. Mustafa
Keyword(s):  
Harmonic Function ◽  
Riemannian Manifolds ◽  
Harmonic Functions ◽  
Horizontal Component ◽  
Harmonic Morphisms

For Riemannian manifoldsMandN, admitting a submersionϕwith compact fibres, we introduce the projection of a function via its decomposition into horizontal and vertical components. By comparing the Laplacians onMandN, we determine conditions under which a harmonic function onU=ϕ−1(V)⊂Mprojects down, via its horizontal component, to a harmonic function onV⊂N.

scholarly journals KNOT SINGULARITIES OF HARMONIC MORPHISMS

2001 ◽  
Vol 44 (1) ◽  
pp. 71-85 ◽  
Author(s):  
Paul Baird
Keyword(s):  
Riemann Surface ◽  
Complex Surface ◽  
Subject Classification ◽  
Harmonic Morphisms ◽  
Singular Set ◽  
Harmonic Morphism ◽  
Complex Curves ◽  
Analytic Curve ◽  
Primary 57M25 ◽  
Straight Lines

AbstractA harmonic morphism defined on $\mathbb{R}^3$ with values in a Riemann surface is characterized in terms of a complex analytic curve in the complex surface of straight lines. We show how, to a certain family of complex curves, the singular set of the corresponding harmonic morphism has an isolated component consisting of a continuously embedded knot.AMS 2000 Mathematics subject classification: Primary 57M25. Secondary 57M12; 58E20

Harmonic morphisms from quaternionic projective spaces

1995 ◽  
Vol 56 (3) ◽  
pp. 327-332 ◽  
Author(s):  
Sigmundur Gudmundsson
Keyword(s):  
Projective Spaces ◽  
Harmonic Morphisms

scholarly journals Biharmonic Maps from Tori into a 2-Sphere

2018 ◽  
Vol 39 (5) ◽  
pp. 861-878
Author(s):  
Zeping Wang ◽  
Ye-Lin Ou ◽  
Hanchun Yang
Keyword(s):  
Biharmonic Maps
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