Constructing isothermal curvature line coordinates on surfaces which admit them

• Autorzy: Eugenio Aulisa , Magdalena Toda , Zeynep Kose
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Isothermal coordinates; Isothermic coordinates; Isothermic surfaces

Kategorie tematyczne

• 53A10: Minimal surfaces, surfaces with prescribed mean curvature

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 11
• Strony: 1982-1993

Daty

wydano

2013-11-01

online

2013-08-23

Twórcy

autor

Eugenio Aulisa

• Texas Tech University

autor

Magdalena Toda

• Texas Tech University

autor

Zeynep Kose

• Texas Tech University

Bibliografia

• [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
• [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
• [4] Ivey T.A., Landsberg J.M., Cartan for Beginners, Grad. Stud. Math., 61, American Mathematical Society, Providence, 2003
• [5] Kose Z., Toda M., Aulisa E., Solving Bonnet problems to construct families of surfaces, Balkan J. Geom. Appl., 2011, 16(2), 70–80
• [6] Lee J.M., Manifolds and Differential Geometry, Grad. Stud. Math., 107, American Mathematical Society, Providence, 2009
• [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

Identyfikatory

DOI

10.2478/s11533-013-0289-6