Constructing isothermal curvature line coordinates on surfaces which admit them
Eugenio Aulisa ; Magdalena Toda ; Zeynep Kose
Open Mathematics, Tome 11 (2013), p. 1982-1993 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

Isothermic parameterizations are synonyms of isothermal curvature line parameterizations, for surfaces immersed in Euclidean spaces. We provide a method of constructing isothermic coordinate charts on surfaces which admit them, starting from an arbitrary chart. One of the primary applications of this work consists of numerical algorithms for surface visualization.

Publié le : 2013-01-01
EUDML-ID : urn:eudml:doc:269099 
@article{bwmeta1.element.doi-10_2478_s11533-013-0289-6,
     author = {Eugenio Aulisa and Magdalena Toda and Zeynep Kose},
     title = {Constructing isothermal curvature line coordinates on surfaces which admit them},
     journal = {Open Mathematics},
     volume = {11},
     year = {2013},
     pages = {1982-1993},
     zbl = {1317.53010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0289-6}
}

Eugenio Aulisa; Magdalena Toda; Zeynep Kose. Constructing isothermal curvature line coordinates on surfaces which admit them. Open Mathematics, Tome 11 (2013) pp. 1982-1993. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0289-6/

[1] Bobenko A.I., Exploring surfaces through methods from the theory of integrable systems: the Bonnet problem, In: Surveys on Geometry and Integrable Systems, Adv. Stud. Pure Math., 51, Math. Soc. Japan, Tokyo, 2008, 1–53 | Zbl 1165.53006

[2] do Carmo M.P., Differential Forms and Applications, Universitext, Springer, Berlin, 1994 http://dx.doi.org/10.1007/978-3-642-57951-6

[3] Chen W., Li H., Bonnet surfaces and isothermic surfaces, Results Math., 1997, 31(1–2), 40–52 http://dx.doi.org/10.1007/BF03322150 | Zbl 0873.53035

[4] Ivey T.A., Landsberg J.M., Cartan for Beginners, Grad. Stud. Math., 61, American Mathematical Society, Providence, 2003 | Zbl 1105.53001

[5] Kose Z., Toda M., Aulisa E., Solving Bonnet problems to construct families of surfaces, Balkan J. Geom. Appl., 2011, 16(2), 70–80 | Zbl 1227.53006

[6] Lee J.M., Manifolds and Differential Geometry, Grad. Stud. Math., 107, American Mathematical Society, Providence, 2009 | Zbl 1190.58001

[7] Pressley A., Elementary Differential Geometry, 2nd ed., Springer Undergrad. Math. Ser., Springer, London, 2010 http://dx.doi.org/10.1007/978-1-84882-891-9 | Zbl 1191.53002