English

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).

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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}
}

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in French

R2 v1 2026-06-22T21:33:32.791Z