Torus Solutions to the Weierstrass-Enneper Representation of Surfaces

Abstract

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.

5 pages