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A representation for pseudoholomorphic surfaces in spheres


Authors: M. Dajczer and Th. Vlachos
Journal: Proc. Amer. Math. Soc. 144 (2016), 3105-3113
MSC (2010): Primary 53C42; Secondary 53A10
DOI: https://doi.org/10.1090/proc/12989
Published electronically: March 18, 2016
MathSciNet review: 3487240
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Abstract: We give a local representation for the pseudoholomorphic surfaces in Euclidean spheres in terms of holomorphic data. Similar to the case of the generalized Weierstrass representation of Hoffman and Osserman for minimal Euclidean surfaces, we assign such a surface in $ \mathbb{S}^{2n}$ to a given set of $ n$ holomorphic functions defined on a simply-connected domain in $ \mathbb{C}$.


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Additional Information

M. Dajczer
Affiliation: Instituto National de Mathemática Pura e Applicada – Estrada Dona Castorina, 110, 22460-320, Rio de Janeiro, Brazil
Email: marcos@impa.br

Th. Vlachos
Affiliation: Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece
Email: tvlachos@uoi.gr

DOI: https://doi.org/10.1090/proc/12989
Received by editor(s): August 20, 2015
Published electronically: March 18, 2016
Communicated by: Lei Ni
Article copyright: © Copyright 2016 American Mathematical Society

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