Binary differential equations associated to congruences of lines in Euclidean 3-space

2023/07/04 by J. W. Bruce, Bruce, J. W., Farid Tari +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Differential Geometry (math.DG) #FOS: Mathematics #Mathematics and Applications #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2307.01887

openalex publication_date 2023/07/04 · openalex created_date 2023/07/07 · openalex updated_date 2026/07/28

Abstract

We study quotients of quadratic forms and associated polar lines in the projective plane. Our results, applied pointwise to quadratic differential forms, shed some light on classical binary differential equations (BDEs) associated to congruences of lines in Euclidean 3-space and allows us to introduce a new one. The new BDE yields a new singular surface in the Euclidean 3-space associated to a congruence of lines. We determine the generic local configurations of the above BDEs on congruences.

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