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arXiv · 1709.01383

Les douze surfaces de Darboux et la trialit{\'e}

Bruno Sévennec
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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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Bruno Sévennec. 2017-09-05. Les douze surfaces de Darboux et la trialit{\'e}. https://arxiv.org/abs/1709.01383

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