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Minimal Darboux transformations
- Source :
- Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry. 58:81-91
- Publication Year :
- 2016
- Publisher :
- Springer Science and Business Media LLC, 2016.
-
Abstract
- We derive a permutability theorem for the Christoffel, Goursat and Darboux transformations of isothermic surfaces. As a consequence we obtain a simple proof of a relation between Darboux pairs of minimal surfaces in Euclidean space, curved flats in the 2-sphere and flat fronts in hyperbolic space.<br />Comment: 9 pages, 2 figures
- Subjects :
- Mathematics - Differential Geometry
Christoffel symbols
Algebra and Number Theory
Minimal surface
Euclidean space
Hyperbolic geometry
Darboux frame
Hyperbolic space
010102 general mathematics
Mathematical analysis
53A10, 37K35 (Primary), 53C42, 53A30, 37K25, 34M45 (Secondary)
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0103 physical sciences
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Mathematics::Differential Geometry
010307 mathematical physics
Geometry and Topology
0101 mathematics
Mathematics
Subjects
Details
- ISSN :
- 21910383 and 01384821
- Volume :
- 58
- Database :
- OpenAIRE
- Journal :
- Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
- Accession number :
- edsair.doi.dedup.....779cae5f8e41c50ac5e4e7e4046d3f02
- Full Text :
- https://doi.org/10.1007/s13366-016-0301-y