A representation for pseudoholomorphic surfaces in spheres

Dajczer, M.; Vlachos, Th.

doi:10.1090/proc/12989

A representation for pseudoholomorphic surfaces in spheres
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by M. Dajczer and Th. Vlachos PDF

Proc. Amer. Math. Soc. 144 (2016), 3105-3113 Request permission

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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