A class of superconformal surfaces
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| 024 | 7 | 0 | |a 10.1007/s10231-014-0436-0 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10231-014-0436-0 | ||
| 245 | 0 | 2 | |a A class of superconformal surfaces |h [Elektronische Daten] |c [M. Dajczer, Th. Vlachos] |
| 520 | 3 | |a Superconformal surfaces in Euclidean space are the one for which the ellipse of curvature at any point is a nondegenerate circle. They can be characterized as the surfaces for which a well-known pointwise inequality relating the intrinsic Gauss curvature with the extrinsic normal and mean curvatures, due to Wintgen (C R Acad Sci Paris T Ser A 288:993-995, 1979) and Guadalupe-Rodríguez (Pac J Math 106:95-103, 1983) for any codimension, reaches equality at all points. In this paper, we show that any pedal surface to a $$2$$ 2 -isotropic Euclidean surface is superconformal. Opposed to almost all known examples, superconformal surfaces in this class are not conformally equivalent to minimal surfaces. Moreover, they can be given in an explicit parametric form since $$2$$ 2 -isotropic surfaces admit a Weierstrass-type representation. | |
| 540 | |a Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2014 | ||
| 690 | 7 | |a Superconformal surface |2 nationallicence | |
| 690 | 7 | |a Ellipse of curvature |2 nationallicence | |
| 690 | 7 | |a Pedal surface |2 nationallicence | |
| 690 | 7 | |a s-Isotropic surface |2 nationallicence | |
| 700 | 1 | |a Dajczer |D M. |u IMPA, Estrada Dona Castorina, 110, 22460-320, Rio de Janeiro, Brazil |4 aut | |
| 700 | 1 | |a Vlachos |D Th |u Mathematics Department, University of Ioannina, 45110, Ioannina, Greece |4 aut | |
| 773 | 0 | |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/6(2015-12-01), 1607-1618 |x 0373-3114 |q 194:6<1607 |1 2015 |2 194 |o 10231 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10231-014-0436-0 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10231-014-0436-0 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Dajczer |D M. |u IMPA, Estrada Dona Castorina, 110, 22460-320, Rio de Janeiro, Brazil |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Vlachos |D Th |u Mathematics Department, University of Ioannina, 45110, Ioannina, Greece |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/6(2015-12-01), 1607-1618 |x 0373-3114 |q 194:6<1607 |1 2015 |2 194 |o 10231 | ||