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Torus solutions to the Weierstrass-Enneper representation of surfaces. (English) Zbl 1422.53008

Summary: In this paper, we present a torus solution to the generalized Weierstrass-Enneper representation of surfaces in \(\mathbb{R}^4\). The key analytical technique will be Bloch wave functions with complex wave vectors. We will also discuss some possible uses of these solutions which derive from their explicit nature, such as Dehn surgery and the physics of exotic smooth structure.
©2019 American Institute of Physics

MSC:

53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
53A07 Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces
53B25 Local submanifolds
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