Geodesic
Helices, Hasimoto Surfaces and Bäcklund Transformations
Canadian mathematical bulletin, Tome 43 (2000) no. 4, pp. 427-439

Voir la notice de l'article provenant de la source Cambridge

DOI

Travelling wave solutions to the vortex filament flow generated by elastica produce surfaces in ${{\mathbb{R}}^{3}}$ that carry mutually orthogonal foliations by geodesics and by helices. These surfaces are classified in the special cases where the helices are all congruent or are all generated by a single screw motion. The first case yields a new characterization for the Bäcklund transformation for constant torsion curves in ${{\mathbb{R}}^{3}}$ , previously derived fromthe well-known transformation for pseudospherical surfaces. A similar investigation for surfaces in ${{H}^{3}}$ or ${{S}^{3}}$ leads to a new transformation for constant torsion curves in those spaces that is also derived from pseudospherical surfaces.
DOI : 10.4153/CMB-2000-051-9
Mots-clés : 53A05, 58F37, 52C42, 58A15, surfaces, filament flow, Bäcklund transformations 
Ivey, Thomas A. Helices, Hasimoto Surfaces and Bäcklund Transformations. Canadian mathematical bulletin, Tome 43 (2000) no. 4, pp. 427-439. doi: 10.4153/CMB-2000-051-9
@article{10_4153_CMB_2000_051_9,
     author = {Ivey, Thomas A.},
     title = {Helices, {Hasimoto} {Surfaces} and {B\"acklund} {Transformations}},
     journal = {Canadian mathematical bulletin},
     pages = {427--439},
     year = {2000},
     volume = {43},
     number = {4},
     doi = {10.4153/CMB-2000-051-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2000-051-9/}
}
TY  - JOUR
AU  - Ivey, Thomas A.
TI  - Helices, Hasimoto Surfaces and Bäcklund Transformations
JO  - Canadian mathematical bulletin
PY  - 2000
SP  - 427
EP  - 439
VL  - 43
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2000-051-9/
DO  - 10.4153/CMB-2000-051-9
ID  - 10_4153_CMB_2000_051_9
ER  - 
%0 Journal Article
%A Ivey, Thomas A.
%T Helices, Hasimoto Surfaces and Bäcklund Transformations
%J Canadian mathematical bulletin
%D 2000
%P 427-439
%V 43
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2000-051-9/
%R 10.4153/CMB-2000-051-9
%F 10_4153_CMB_2000_051_9

Cité par Sources :