Trigonal minimal surfaces in flat tori

Details Trigonal minimal surfaces in flat tori Trigonal minimal surfaces in flat tori

2007-03-21

arxiv.org/abs/math/0703622v2

Mathematics

Differential Geometry

21pages. to appear in Pacific Journal of Mathematics

Scientific paper

In this paper, we study trigonal minimal surfaces in flat tori. First, we show a topological obstruction similar to that of hyperelliptic minimal surfaces. Actually, the genus of trigonal minimal surface in 3-dimensional flat torus must be 1 (mod 3). Next, we construct an explicit example in the higher codimensional case. This surface satisfies good properties and is theoretically distinct from traditional examples.

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