We exhibit several transformations of surfaces $M$ in $\mathbb{R}^4$: a
transformation of flat surfaces that gives surfaces with flat normal bundle
(semiumbilical surfaces); and its inverse that from a semiumbilical surface
obtains a flat surface; then a one-parameter family of transformations $f$ on
flat semiumbilical immersed surfaces (FSIS), such that $df(T_pM)$ is totally
orthogonal to $T_pM,$ and that give FSIS. This family satisfies a Bianchi type
of permutability property.
Publié le : 2008-04-15
Classification:
flat, semiumbilical surfaces in $\mathbb{R}^4$,
Bianchi permutability,
Bäcklund transformation,
evolute,
53A05
@article{1216247096,
author = {Montesinos-Amilibia , Angel},
title = {Transformations between surfaces in $\mathbb{R}^4$ with
flat normal and/or tangent bundles},
journal = {Rev. Mat. Iberoamericana},
volume = {24},
number = {2},
year = {2008},
pages = { 71-90},
language = {en},
url = {http://dml.mathdoc.fr/item/1216247096}
}
Montesinos-Amilibia , Angel. Transformations between surfaces in $\mathbb{R}^4$ with
flat normal and/or tangent bundles. Rev. Mat. Iberoamericana, Tome 24 (2008) no. 2, pp. 71-90. http://gdmltest.u-ga.fr/item/1216247096/