Les douze surfaces de Darboux et la trialit{\'e}
Differential Geometry
2021-10-01 v2
Abstract
The purpose of this article is to give a geometric interpretation to the so-called "twelve surfaces of Darboux", or "Darboux wreath", which appear by applying repeatedly certain simple transformations to a given infinitesimal isometric deformation of a surface in euclidean three space. This interpretation is a differential-geometric version of triality, concerning totally isotropic surfaces immersed in the real 6-dimensional projective quadric defined by a quadratic form of neutral signature (4,4).
Cite
@article{arxiv.1709.01383,
title = {Les douze surfaces de Darboux et la trialit{\'e}},
author = {Bruno Sévennec},
journal= {arXiv preprint arXiv:1709.01383},
year = {2021}
}
Comments
in French