Connectedness of the space of minimal 2-spheres in S2m(l)

Motoko Kotani

doi:10.1090/S0002-9939-1994-1169040-9

Connectedness of the space of minimal 2-spheres in S^2m(l)

Motoko Kotani

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

Abstract

Loo's theorem asserts that the space of all branched minimal 2- spheres of degree d in S⁴(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.

Original language	English
Pages (from-to)	803-810
Number of pages	8
Journal	Proceedings of the American Mathematical Society
Volume	120
Issue number	3
DOIs	https://doi.org/10.1090/S0002-9939-1994-1169040-9
Publication status	Published - 1994 Mar
Externally published	Yes

Keywords

Branched minimal 2-spheres
Directrix curves
Isotropic curves

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

Access to Document

10.1090/S0002-9939-1994-1169040-9

Cite this

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abstract = "Loo's theorem asserts that the space of all branched minimal 2- spheres of degree d in S4(1) is connected. The main theorem in this paper is that the assertion is still true for S2m(1). It is shown that any branched minimal 2-sphere in S2m(1) can be deformed, preserving its degree, to a meromorphic function.",

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KW - Isotropic curves

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