Proceedings of the International Conference on Geometry, Integrability and Quantization

Deformations of Minimal Surfaces

Ivailo M. Mladenov and Borislav Angelov

Abstract

Here we combine group-theoretical and differential-geometric techniques for considerations of minimal surface deformations in the ordinary three-dimensional space. This approach allows a consideration of a novel family of transformations generated by complex rotations. The resulting generalized deformations are compared with the well-known Bonnet and Goursat transformations and illustrated via the Schwarz skew quadrilateral to provide a clarification of their geometrical origin.

Article information

Source
Proceedings of the International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov and Gregory L. Naber, eds. (Sofia: Coral Press Scientific Publishing, 2000), 163-174

Dates
First available in Project Euclid: 5 June 2015

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1433524885

Digital Object Identifier
doi:10.7546/giq-1-2000-163-174

Mathematical Reviews number (MathSciNet)
MR1758160

Zentralblatt MATH identifier
1040.53004

Citation

Mladenov, Ivailo M.; Angelov, Borislav. Deformations of Minimal Surfaces. Proceedings of the International Conference on Geometry, Integrability and Quantization, 163--174, Coral Press Scientific Publishing, Sofia, Bulgaria, 2000. doi:10.7546/giq-1-2000-163-174. https://projecteuclid.org/euclid.pgiq/1433524885


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