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Transactions of the American Mathematical Society

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On minimal immersions of $ S\sp{2}$ into $ S\sp{2m}$

Author: Jo ao Lucas Marquês Barbosa
Journal: Trans. Amer. Math. Soc. 210 (1975), 75-106
MSC: Primary 53C40; Secondary 32H25
MathSciNet review: 0375166
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Abstract: The study of minimal immersions of the $ 2$-sphere into the standard $ n$-sphere of the euclidean space has been better accomplished by associating to each such immersion a certain holomorphic curve. This has been done in several ways in the literature. In the present paper we explore this technique applying some knowledge about the topological and analytical invariants of the particular set of holomorphic curves used to obtain further results. Some new examples are provided, a beginning of a general description of such immersions is given and a rigidity theorem is proved.

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Article copyright: © Copyright 1975 American Mathematical Society