دورية أكاديمية
Relating second order geometry of manifolds through projections and normal sections
| العنوان: | Relating second order geometry of manifolds through projections and normal sections |
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| المؤلفون: | Riul, P. Benedini, Sinha, R. Oset |
| بيانات النشر: | Universitat Autònoma de Barcelona, Departament de Matemàtiques |
| سنة النشر: | 2021 |
| المجموعة: | Project Euclid (Cornell University Library) |
| مصطلحات موضوعية: | projections, normal sections, curvature locus, immersed surfaces, immersed $3$-manifolds, singular corank $1$ manifolds, 57R45, 53A05, 58K05 |
| الوصف: | We use normal sections to relate the curvature locus of regular (resp. singular corank $1$) $3$-manifolds in $\mathbb{R}^6$ (resp.\ $\mathbb R^5$) with regular (resp.\ singular corank $1$) surfaces in $\mathbb R^5$ (resp. $\mathbb R^4$). For example, we show how to generate a Roman surface by a family of ellipses different to Steiner's way. We also study the relations between the regular and singular cases through projections. We show that there is a commutative diagram of projections and normal sections which relates the curvature loci of the different types of manifolds, and therefore, that the second order geometry of all of them is related. In particular, we define asymptotic directions for singular corank $1$ $3$-manifolds in $\mathbb R^5$ and relate them to asymptotic directions of regular $3$-manifolds in $\mathbb R^6$ and singular corank $1$ surfaces in $\mathbb R^4$. |
| نوع الوثيقة: | text |
| وصف الملف: | application/pdf |
| اللغة: | English |
| تدمد: | 0214-1493 2014-4350 |
| العلاقة: | https://projecteuclid.org/euclid.pm/1607655922Test; Publ. Mat. 65, no. 1 (2021), 389-407 |
| DOI: | 10.5565/PUBLMAT6512114 |
| الإتاحة: | https://doi.org/10.5565/PUBLMAT6512114Test https://projecteuclid.org/euclid.pm/1607655922Test |
| حقوق: | Copyright 2021 Universitat Autònoma de Barcelona, Departament de Matemàtiques |
| رقم الانضمام: | edsbas.767D6108 |
| قاعدة البيانات: | BASE |
| تدمد: | 02141493 20144350 |
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| DOI: | 10.5565/PUBLMAT6512114 |