Discrete special isothermic surfaces

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• 作者：F. Burstall ; U. Hertrich-Jeromin ; W. Rossman ; S. Santos
• 关键词：Isothermic surface ; Darboux transformation ; Lawson correspondence ; B?cklund transformation ; Polynomial conserved quantity ; Constant mean curvature ; 53A10 ; 53C42 ; 53A30 ; 37K25 ; 37K35
• 刊名：Geometriae Dedicata
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：174
• 期：1
• 页码：1-11
• 全文大小：323 KB
• 参考文献：1. Bernstein, H.: Non-special, non-canal isothermic tori with spherical lines of curvature. Trans. AMS 353, 2245-274 (2001) CrossRef
  2. Bianchi, L.: Ricerche sulle superficie isoterme e sulla deformazione delle quadriche. Ann. Math. 11, 93-57 (1904)
  3. Bobenko, A., Pinkall, U.: Discretization of surfaces and integrable systems. Oxf. Lect. Ser. Math. Appl. 16, 3-8 (1999)
  4. Bobenko, A., Suris, Y.: Discrete Differential Geometry. Integrable structure; Grad Stud Math 98. Amer Math Soc, Providence, RI (2008)
  5. Bobenko, A., Hertrich-Jeromin, U., Lukyanenko, I.: Discrete constant mean curvature nets in space forms: Steiner’s formula and Christoffel duality. Discret. Comput. Geom. (2014)
  6. Burstall, F., Hertrich-Jeromin, U., Rossman, W., Santos, S.: Discrete surfaces of constant mean curvature. RIMS Kokyuroku 1880, 133-79 (2014)
  7. Burstall, F., Santos, S.: Special isothermic surfaces of type \(d\) . J. Lond. Math. Soc. 85, 571-91 (2012) CrossRef
  8. Burstall, F., Hertrich-Jeromin, U., Rossman, W.: Discrete linear Weingarten surfaces. arXiv:1406.1293 (2014)
  9. Eisenhart, L.: Transformations of Surfaces. Princeton Univ Press, Princeton (1923)
  10. Hertrich-Jeromin, U., Hoffmann, T., Pinkall, U.: A discrete version of the Darboux transform for isothermic surfaces. Oxf. Lect. Ser. Math. Appl. 16, 59-1 (1999)
  11. Hertrich-Jeromin, U.: Introduction to M?bius Differential Geometry; London Math Soc Lect Note Series 300. Cambridge Univ Press, Cambridge (2003) CrossRef
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Geometry
  
• 出版者：Springer Netherlands
• ISSN：1572-9168

文摘

We discuss special isothermic nets of type \(N\) , a new class of discrete isothermic nets, generalizing isothermic nets with constant mean curvature in spaceforms. In the case \(N=2\) these are the discrete analogues of Bianchi’s special isothermic surfaces that can be regarded as the origin of the rich transformation theory of isothermic surfaces. Accordingly, special isothermic nets come with B?cklund transformations and a Lawson correspondence. The notion of complementary nets naturally occurs and sheds further light on the relation between geometry and integrability.