Lines of curvature on quadric hypersurfaces of ℝ 4

J. Sotomayor; R. Garcia

doi:10.1134/S1995080216030203

Lines of curvature on quadric hypersurfaces of ℝ⁴

Authors: Sotomayor J.¹, Garcia R.¹
Affiliations:
1. Instituto de Matemática e Estatística
Issue: Vol 37, No 3 (2016)
Pages: 288-306
Section: Article
URL: https://journals.rcsi.science/1995-0802/article/view/197731
DOI: https://doi.org/10.1134/S1995080216030203
ID: 197731

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Abstract
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Abstract

We describe the geometric structures of the lines of principal curvature and the partially umbilic singularities of the three-dimensional non compact generic quadric hypersurfaces of R⁴. This includes the ellipsoidal hyperboloids of one and two sheets and the toroidal hyperboloids. The present study complements the analysis of the compact ellipsoidal hypersurfaces carried out in [9].

Keywords

Partially umbilic point, quadrics, principal lines, principal configuration

About the authors

J. Sotomayor

Instituto de Matemática e Estatística

Author for correspondence.
Email: sotp@ime.usp.br
Brazil, 1010 Cidade Universitária, São Paulo S. P, CEP, 05508-090

R. Garcia