Curves with Prescribed Curvature and Associated Surfaces

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In this work, we study surfaces with a canonical principal direction (CPD surfaces) under the simultaneous prescription of two extrinsic geometric invariants: one principal curvature and the support function. Based on these prescriptions, we reformulate the first and second fundamental forms, which...

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Detalles Bibliográficos
Autores: V. Corro, Armando M., Lopes Ferro, Marcelo
Formato: artículo
Fecha de Publicación:2025
Institución:Universidad Nacional de Trujillo
Repositorio:Revistas - Universidad Nacional de Trujillo
Lenguaje:inglés
OAI Identifier:oai:ojs.revistas.unitru.edu.pe:article/7099
Enlace del recurso:https://revistas.unitru.edu.pe/index.php/SSMM/article/view/7099
Nivel de acceso:acceso abierto
Materia:Superficies CPD
curvatura prescrita
catenarias
dirección principal
CPD surfaces
prescribed curvature
catenaries
principal direction
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spelling Curves with Prescribed Curvature and Associated SurfacesCurvas con curvatura prescrita y superficies asociadasV. Corro, Armando M.Lopes Ferro, MarceloSuperficies CPDcurvatura prescritacatenariasdirección principalCPD surfacesprescribed curvaturecatenariesprincipal directionIn this work, we study surfaces with a canonical principal direction (CPD surfaces) under the simultaneous prescription of two extrinsic geometric invariants: one principal curvature and the support function. Based on these prescriptions, we reformulate the first and second fundamental forms, which enables us to construct explicit examples of such surfaces. Finally, we show that when the curvature of the profile curve is constant, that is, when one of the principal curvatures is constant, the corresponding CPD surface is a tubular surface. En este trabajo se estudian las superficies con una dirección principal canónica (superficies CPD) bajo la prescripción simultánea de dos invariantes geométricos extrínsecos: una curvatura principal y la función soporte. A partir de dichas prescripciones, se reescriben las primeras y segundas formas fundamentales, lo que permite presentar ejemplos explícitos de este tipo de superficies. Finalmente, se demuestra que, cuando la curvatura de la curva de perfil es constante, es decir, cuando una de las curvaturas principales es constante, la superficie CPD resulta ser una superficie tubular.National University of Trujillo - Academic Department of Mathematics2025-12-27info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://revistas.unitru.edu.pe/index.php/SSMM/article/view/7099Selecciones Matemáticas; Vol. 12 No. 02 (2025): August - December; 413 - 422Selecciones Matemáticas; Vol. 12 Núm. 02 (2025): Agosto - Diciembre; 413 - 422Selecciones Matemáticas; v. 12 n. 02 (2025): Agosto - Dezembro; 413 - 4222411-1783reponame:Revistas - Universidad Nacional de Trujilloinstname:Universidad Nacional de Trujilloinstacron:UNITRUenghttps://revistas.unitru.edu.pe/index.php/SSMM/article/view/7099/7115https://creativecommons.org/licenses/by/4.0info:eu-repo/semantics/openAccessoai:ojs.revistas.unitru.edu.pe:article/70992025-12-27T01:09:48Z
dc.title.none.fl_str_mv Curves with Prescribed Curvature and Associated Surfaces
Curvas con curvatura prescrita y superficies asociadas
title Curves with Prescribed Curvature and Associated Surfaces
spellingShingle Curves with Prescribed Curvature and Associated Surfaces
V. Corro, Armando M.
Superficies CPD
curvatura prescrita
catenarias
dirección principal
CPD surfaces
prescribed curvature
catenaries
principal direction
title_short Curves with Prescribed Curvature and Associated Surfaces
title_full Curves with Prescribed Curvature and Associated Surfaces
title_fullStr Curves with Prescribed Curvature and Associated Surfaces
title_full_unstemmed Curves with Prescribed Curvature and Associated Surfaces
title_sort Curves with Prescribed Curvature and Associated Surfaces
dc.creator.none.fl_str_mv V. Corro, Armando M.
Lopes Ferro, Marcelo
author V. Corro, Armando M.
author_facet V. Corro, Armando M.
Lopes Ferro, Marcelo
author_role author
author2 Lopes Ferro, Marcelo
author2_role author
dc.subject.none.fl_str_mv Superficies CPD
curvatura prescrita
catenarias
dirección principal
CPD surfaces
prescribed curvature
catenaries
principal direction
topic Superficies CPD
curvatura prescrita
catenarias
dirección principal
CPD surfaces
prescribed curvature
catenaries
principal direction
description In this work, we study surfaces with a canonical principal direction (CPD surfaces) under the simultaneous prescription of two extrinsic geometric invariants: one principal curvature and the support function. Based on these prescriptions, we reformulate the first and second fundamental forms, which enables us to construct explicit examples of such surfaces. Finally, we show that when the curvature of the profile curve is constant, that is, when one of the principal curvatures is constant, the corresponding CPD surface is a tubular surface. 
publishDate 2025
dc.date.none.fl_str_mv 2025-12-27
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://revistas.unitru.edu.pe/index.php/SSMM/article/view/7099
url https://revistas.unitru.edu.pe/index.php/SSMM/article/view/7099
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv https://revistas.unitru.edu.pe/index.php/SSMM/article/view/7099/7115
dc.rights.none.fl_str_mv https://creativecommons.org/licenses/by/4.0
info:eu-repo/semantics/openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/4.0
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv National University of Trujillo - Academic Department of Mathematics
publisher.none.fl_str_mv National University of Trujillo - Academic Department of Mathematics
dc.source.none.fl_str_mv Selecciones Matemáticas; Vol. 12 No. 02 (2025): August - December; 413 - 422
Selecciones Matemáticas; Vol. 12 Núm. 02 (2025): Agosto - Diciembre; 413 - 422
Selecciones Matemáticas; v. 12 n. 02 (2025): Agosto - Dezembro; 413 - 422
2411-1783
reponame:Revistas - Universidad Nacional de Trujillo
instname:Universidad Nacional de Trujillo
instacron:UNITRU
instname_str Universidad Nacional de Trujillo
instacron_str UNITRU
institution UNITRU
reponame_str Revistas - Universidad Nacional de Trujillo
collection Revistas - Universidad Nacional de Trujillo
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1852864028407234560
score 13.91342
Curves with Prescribed Curvature and Associated Surfaces
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