Table of Contents
ISRN Geometry
Volume 2011 (2011), Article ID 943462, 19 pages
http://dx.doi.org/10.5402/2011/943462
Research Article

Minimal Surfaces with Only Horizontal Symmetries

1CMCC, UFABC, Rua Santa Adélia 166, Bl.A-2, 09210-170 Santo André, SP, Brazil
2DM, UFSCar, Rua Washington Luís km 235, 13565-905 São Carlos, SP, Brazil

Received 6 April 2011; Accepted 11 May 2011

Academic Editors: L. V. Bogdanov, G. Martin, and C. Qu

Copyright © 2011 Márcio Fabiano da Silva et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The Schwarz reflection principle states that a minimal surface 𝑆 in 3 is invariant under reflections in the plane of its principal geodesics and also invariant under 180°-rotations about its straight lines. We find new examples of embedded triply periodic minimal surfaces for which such symmetries are all of horizontal type.