A representation for pseudoholomorphic surfaces in spheres

2015/08/04 by Dajczer, M., Vlachos, Th. · 1 citation
#53A10 #53C42 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1508.00753

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, we assign such a surface in \Sf²ⁿ to a given set of n holomorphic functions defined on a simply-connected domain in \C.

Cited by

• Local Wintgen ideal submanifolds

Related

• Spherical type surfaces via support function
• Holomorphic structures for surfaces in Euclidean n-space
• Minimal surfaces in spheres and a Ricci-like condition
• Complex analysis and a class of Weingarten surfaces
• Weingarten Surfaces Associated to Laguerre Minimal Surfaces