Harmonic morphisms

2018 ◽  
pp. 191-209
Keyword(s):  
1999 ◽  
Vol 94 (2) ◽  
pp. 1263-1269 ◽  
Author(s):  
J. C. Wood

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

2012 ◽  
Vol 2012 ◽  
pp. 1-8
Author(s):  
M. T. Mustafa

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.


2001 ◽  
Vol 44 (1) ◽  
pp. 71-85 ◽  
Author(s):  
Paul Baird

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


1995 ◽  
Vol 56 (3) ◽  
pp. 327-332 ◽  
Author(s):  
Sigmundur Gudmundsson

2006 ◽  
Vol 14 (5) ◽  
pp. 847-881 ◽  
Author(s):  
Eric Loubeau ◽  
Radu Pantilie

2000 ◽  
Vol 42 (1) ◽  
pp. 25-29 ◽  
Author(s):  
Eric Loubeau ◽  
Stefano Montaldo

We prove that exponentially harmonic morphisms are precisely the Riemannian submersions with minimal fibres.1991 Mathematics Subject Classification 58E20.


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