New Flat Surfaces in S3

Authors

  • Armando M. V. Corro IME, Universidade Federal de Goiás, Caixa Postal 131, 74001-970, Goiania, GO, Brazil.
  • Marcelo Lopes Ferro IME, Universidade Federal de Goiás, Caixa Postal 131, 74001-970, Goiania, GO, Brazil.

DOI:

https://doi.org/10.17268/sel.mat.2021.01.07

Keywords:

Flat surfaces, Ribaucour transformations, 3-sphere, flat torus, complete surface

Abstract

In this paper, we consider a method of constructing flat surfaces based on Ribaucour transformations in S3. By applying the theory to the flat torus, we obtain a family of complete flat surfaces in S3 which is determined by several parameters. We provide explicit examples.

References

Aledo JA, Gálvez JA, Mira P. A D’Alembert Formula for Flat Surfaces in the 3-Sphere. Journal of Geometric Analysis. 2009; 19:211-232.

Bianchi L. Lezioni di geometria Differenziale. Terza Edicione. Nicola Zanichelli Editore; 1927.

Corro AMV, Ferreira WP, Tenenblat K. On Ribaucour transformations for hypersurfaces. Mat. Contemp. 1999; 17:137-160.

Corro AMV, Ferreira WP, Tenenblat K. Ribaucour transformations for Constant mean curvature and linearWeingarten surfaces. Pacific Journal of Mathematics. 2003; 212(2):265-296.

Corro AMV, Ferreira WP, Tenenblat K. Minimal surfaces obtained by Ribaucour transformations. Geometriae Dedicata, Nettherlands. 2003; 96(1):117-150.

Corro AMV, Tenenblat K. Ribaucour transformation revisited. Comum. Geom. 2004; 12(5):1055-1082.

Corro AMV. Generalized Weingarten surfaces of Bryant type in Hiperbolic 3-space. Mat. Contemp. 2006; 30:71-89.

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Published

2021-07-29

How to Cite

V. Corro, A. M., & Lopes Ferro, M. (2021). New Flat Surfaces in S3. Selecciones Matemáticas, 8(01), 75 - 82. https://doi.org/10.17268/sel.mat.2021.01.07

Issue

Vol. 8 No. 01 (2021): January-July

Section

Articles

License

Copyright (c) 2021 Armando M. V. Corro, Marcelo Lopes Ferro

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