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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Connectedness of the space of minimal $ 2$-spheres in $ S\sp {2m}(1)$


Author: Motoko Kotani
Journal: Proc. Amer. Math. Soc. 120 (1994), 803-810
MSC: Primary 58E20; Secondary 53C42, 58D27
MathSciNet review: 1169040
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Abstract: Loo's theorem asserts that the space of all branched minimal $ 2$-spheres of degree $ d$ in $ {S^4}(1)$ is connected. The main theorem in this paper is that the assertion is still true for $ {S^{2m}}(1)$. It is shown that any branched minimal $ 2$-sphere in $ {S^{2m}}(1)$ can be deformed, preserving its degree, to a meromorphic function.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1169040-9
PII: S 0002-9939(1994)1169040-9
Keywords: Branched minimal $ 2$-spheres, directrix curves, isotropic curves
Article copyright: © Copyright 1994 American Mathematical Society