Ribaucour coordinates

Francis E. Burstall1, Udo Hertrich-Jeromin2, Margarida Miró2
1Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK
2Vienna University of Technology, Wiedner Hauptstraße 8-10/104, 1040, Vienna, Austria

Tóm tắt

Từ khóa


Tài liệu tham khảo

Blaschke, W.: Vorlesungen über Differentialgeometrie III. Grundlehren, Vol. XXIX. Springer, Berlin (1929)

Bo, P., Kilian, M., Pottmann, H., Wallner, J., Wang, W.: Circular arc structures. ACM Trans. Graph. Proc. SIGGRAPH 30, 101 (2011)

Bobenko, A., Hertrich-Jeromin, U.: Orthogonal nets and Clifford algebras. Tôhoku Math. Publ. 20, 7–22 (2001)

Bobenko, A., Huhnen-Venedy, E.: Curvature line parametrized surfaces and orthogonal coordinate systems: discretization with Dupin cyclides. Geom. Dedicata 159, 207–237 (2012)

Burstall, F., Calderbank, D.: Conformal submanifold geometry I–III (2010). EPrint arXiv:1006.5700

Burstall, F., Hertrich-Jeromin, U.: The Ribaucour transformation in Lie sphere geometry. Differ. Geom. Appl. 24, 503–520 (2006)

Burstall, F., Hertrich-Jeromin, U., Müller, C., Rossman, W.: Semi-discrete isothermic surfaces. Geom. Dedicata 183, 43–58 (2016)

Corro, A., Tenenblat, K.: Ribaucour transformations revisited. Commun. Anal. Geom. 12, 1055–1082 (2004)

Dajczer, M., Florit, L., Tojeiro, R.: The vectorial Ribaucour transformation for submanifolds and its applications. Trans. Am. Math. Soc. 359, 4977–4997 (2007)

de Lima, L., Roitman, P.: Constant mean curvature one surfaces in hyperbolic 3-space using the Bianchi–Calò method. Ann. Braz. Acad. Sci. 74, 19–24 (2002)

Hertrich-Jeromin, U., Rossman, W., Szewieczek, G.: Discrete channel surfaces (in preparation)

Hertrich-Jeromin, U.: Introduction to Möbius differential geometry. London Mathematical Society Lecture Note Series, Vol. 300. Cambridge University Press, Cambridge (2003)

Müller, C., Wallner, J.: Semi-discrete isothermic surfaces. Res. Math. 63, 1395–1407 (2013)

Pember, M., Szewieczek, G.: Channel surfaces in Lie sphere geometry (2017). EPrint arXiv:1709.02224