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Harmonic maps of spheres and equivariant theory
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Ratto, Andrea (1987) Harmonic maps of spheres and equivariant theory. PhD thesis, University of Warwick.

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Official URL: http://webcat.warwick.ac.uk/record=b1452023~S1
Abstract
In Chapter I we produce many new harmonic maps of spheres by the qualitative study of the pendulum equations for the join and the Hopf construction. In particular, we obtain
Corollary 1.7.1.
Let Φ1 : Sp > Sr be any harmonic homogeneous polynomial of degree greater or equal than two, and let Φ2 be the identity map id : Sq > Sq. Then the (q+1)suspension of Φ1 is harmonically representable by an equivariant map of the form Φ1 * Φ2 if and only if q=0 ....5.
Corollary 1.11.1.
Let [f] E ΠSp be a stable class in the image of the stable Jho momorphism Jp :Πp (0) > ΠSp, p >= 6. Then there exists q > p such that [f] can be represented by a harmonic map Φ : Sp+q+1 > Sq+1.
In Chapter II we illustrate equivariant theory and study the rendering problems: in particular, we show that the restriction q=o ...5 in Corollary 1.7.1. can be removed provided that the domain is given a suitable riemannian metric; then, for istance, the groups Πn(Sn) = Z can be rendered harmonic for every n.
In Chapter III we describe applications of equivariant theory to the study of Dirichlet problems and warped products; and extensions of the theory to spaces with conical singularities.
Item Type:  Thesis (PhD)  

Subjects:  Q Science > QA Mathematics  
Library of Congress Subject Headings (LCSH):  Harmonic maps, Sphere  
Official Date:  September 1987  
Dates: 


Institution:  University of Warwick  
Theses Department:  Mathematics Institute  
Thesis Type:  PhD  
Publication Status:  Unpublished  
Supervisor(s)/Advisor:  Eells, James, 19262007  
Extent:  iv, 159 leaves  
Language:  eng 
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