The Existence of rG Family and tG Family, and Their Geometric Invariants

Norio Ejiri and Toshihiro Shoda
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Norio Ejiri: Department of Mathematics, Meijo University, Tempaku, Nagoya 468-8502, Japan
Toshihiro Shoda: Faculty of Education, Saga University, 1 Honjo-machi, Saga 840-8502, Japan

Mathematics, 2020, vol. 8, issue 10, 1-39

Abstract: In the 1990s, physicists constructed two one-parameter families of compact oriented embedded minimal surfaces in flat three-tori by using symmetries of space groups, called the rG family and tG family. The present work studies the existence of the two families via the period lattices. Moreover, we will consider two kinds of geometric invariants for the two families, namely, the Morse index and the signature of a minimal surface. We show that Schwarz P surface, D surface, Schoen’s gyroid, and the Lidinoid belong to a family of minimal surfaces with Morse index 1.

Keywords: minimal surfaces; flat tori; Morse index; signature (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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