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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The space of harmonic maps of $ S\sp 2$ into $ S\sp 4$


Author: Bonaventure Loo
Journal: Trans. Amer. Math. Soc. 313 (1989), 81-102
MSC: Primary 58E20; Secondary 58D15
MathSciNet review: 962283
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Abstract: Every branched superminimal surface of area $ 4\pi d$ in $ {S^4}$ is shown to arise from a pair of meromorphic functions $ ({f_1},{f_2})$ of bidegree $ (d,d)$ such that $ {f_1}$ and $ {f_2}$ have the same ramification divisor. Conditions under which branched superminimal surfaces can be generated from such pairs of functions are derived. For each $ d \geq 1$ the space of harmonic maps (i.e branched superminimal immersions) of $ {S^2}$ into $ {S^4}$ of harmonic degree $ d$ is shown to be a connected space of complex dimension $ 2d + 4$ .


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DOI: http://dx.doi.org/10.1090/S0002-9947-1989-0962283-9
PII: S 0002-9947(1989)0962283-9
Article copyright: © Copyright 1989 American Mathematical Society