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

 

Minimal immersions of $ 2$-spheres in $ S\sp{4}$


Author: Ernst A. Ruh
Journal: Proc. Amer. Math. Soc. 28 (1971), 219-222
MSC: Primary 53.75
MathSciNet review: 0271880
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Abstract: The classification of isolated singularities of minimal varieties leads to the study of minimal manifolds in the $ n$-sphere. The object of this paper is to show that a minimal $ 2$-sphere in $ {S^4}$ with trivial normal bundle is the standard $ 2$-sphere.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0271880-X
PII: S 0002-9939(1971)0271880-X
Keywords: Codazzi equations, Euler number, minimal immersion, normal bundle, parallel mean curvature
Article copyright: © Copyright 1971 American Mathematical Society