Trigonal minimal surfaces in flat tori

Toshihiro Shoda

Vol. 232 (2007), No. 2, 401–422

DOI: 10.2140/pjm.2007.232.401

Abstract

We study trigonal minimal surfaces in flat tori. showing first a topological obstruction similar to that of hyperelliptic minimal surfaces: the genus of a trigonal minimal surface in a 3-dimensional flat torus must be 1 (mod 3). Next we construct an explicit example of a trigonal minimal surface in a 4-dimensional flat torus. This surface satisfies good properties and is theoretically distinct from earlier examples.

Keywords

minimal surfaces, flat tori, trigonal curves

Mathematical Subject Classification 2000

Primary: 53A10, 53C42

Milestones

Received: 22 March 2006

Revised: 26 February 2007

Accepted: 7 March 2007

Published: 1 October 2007