Relating second order geometry of manifolds through projections and normal sections
Benedini Riul, Pedro (Universidade Federal de S˜ao Carlos. Departamento de Matem'atica)
Oset Sinha, Raul (Universitat de València. Departament de Matemàtiques)

Date:	2021
Abstract:	We use normal sections to relate the curvature locus of regular (resp. singular corank 1) 3-manifolds in R6 (resp. R5) with regular (resp. singular corank 1) surfaces in R5 (resp. R4 ). 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 R5 and relate them to asymptotic directions of regular 3-manifolds in R6 and singular corank 1 surfaces in R4.
Grants:	Ministerio de Ciencia e Innovación PGC2018-094889-B-I00
Note:	P. Benedini Riul was supported by FAPESP Grant 2019/00194-6. R.Oset Sinha was partially supported by MICINN Grant PGC2018-094889-B-I00 and GVA Grant AICO/2019/024.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Projections ; Normal sections ; Curvature locus ; Immersed surfaces ; Immersed 3-manifolds ; Singular corank 1 manifolds
Published in:	Publicacions matemàtiques, Vol. 65 Núm. 1 (2021) , p. 389-407 (Articles) , ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/384546
DOI: 10.5565/PUBLMAT6512114
DOI: 10.5565/publicacionsmatematiques.v65i1.384546

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