Curvature lines on orthogonal surfaces of R3 and Joachimsthal Theorem

In this paper is studied; as a complement of Joachimsthal theorem; the behavior of curvature lines near a principal cycle common to two orthogonal surfaces.

Autores:
Garcia, Ronaldo A.
Tipo de recurso:
Article of investigation
Fecha de publicación:
2005
Institución:
Universidad Sergio Arboleda
Repositorio:
Repositorio U. Sergio Arboleda
Idioma:
spa
OAI Identifier:
oai:repository.usergioarboleda.edu.co:11232/310
Acceso en línea:
https://doi.org/10.22518/16578953.800
http://hdl.handle.net/11232/310
Palabra clave:
Geometría diferencial
Superficies
Topología
Teorema Joachimsthal
Curvas
principal cycle
curvature lines
MSC: 53C12
34D30
53A05
37C75
Rights
openAccess
License
Atribución-NoComercial-SinDerivadas 2.5 Colombia (CC BY-NC-ND 2.5 CO)
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spelling Atribución-NoComercial-SinDerivadas 2.5 Colombia (CC BY-NC-ND 2.5 CO)http://creativecommons.org/licenses/by-nc-nd/2.5/co/Abierto (Texto Completo)info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Garcia, Ronaldo A.20052015-07-22T21:13:56Z2016-05-11T14:34:51Z2017-05-16T17:17:01Z2015-07-22T21:13:56Z2016-05-11T14:34:51Z2017-05-16T17:17:01Z2005-06-20Garcia, R. A. (2005). Curvature lines on orthogonal surfaces of R3 and Joachimsthal Theorem. Civilizar Ciencias Sociales y Humanas, 5(8), 141-151.1657-8953https://doi.org/10.22518/16578953.800instname:Universidad Sergio Arboledareponame:Repositorio Institucional Universidad Sergio Arboledarepourl:https://repository.usergioarboleda.edu.co/http://hdl.handle.net/11232/310In this paper is studied; as a complement of Joachimsthal theorem; the behavior of curvature lines near a principal cycle common to two orthogonal surfaces.11Digitalapplication/pdfdocumentosspaUniversidad Sergio ArboledaRevista Civilizar Ciencias Sociales y Humanas; vol. 5, núm. 8 (2005)M. Bergerand B. Gostiaux Introduction to Differential Geometry, Springer Verlag,New York, (1987).M. do Carmo, Differential Geometry of curves and surfaces, Prentice Hall, New Jersey,(1976).G. DarbouxLe ̧cons sur la Th ́eorie des Surfaces, vol. I, IV, Gauthiers Villars, (1896).C. GutierrezandJ. Sotomayor,Closed principal lines and bifurcation, Bull. Braz.Math. Soc.17, 1986, pp. 1-19R. GarciaandJ. SotomayorLectures Notes on Qualitative Theory of DifferentialEquations of Classical Geometry, Notas de Curso, IME/UFG, (2000).C. GutierrezandJ. Sotomayor,Lines of Curvature and Umbilic Points on Surfaces,Brazilian 18thMath. Coll., IMPA, 1991, Reprinted asStructurally Configurations ofLines of Curvature and Umbilic Points on Surfaces, Monografias del IMCA, (1998).H. Hopf,Differential Geometry in the Large, Springer Lecture Notes in Mathematics,vol. 1000, (1983).D. HilbertandS. Cohn Vossen Geometry and the Imagination, Chelsea, (1952).M. SpivakA Comprehensive Introduction to Differential Geometry, vol.III, V, Publishof Perish Berkeley, (1979).M. SpivakA Comprehensive Introduction to Differential Geometry, vol.III, V, Publishof Perish Berkeley, (1979).A. Gray, L. CordeiroandM. Fernández,Geometría diferencial de curvas y superficies, con Mathematica, Addison-Wesley Iberoamericana, (1995).G. MongeJourn. de l’Ecole Polytech,IIe, (1796),Applications de l’Algebre a la Geometrie, Paris, (1850).Civilizar Ciencias Sociales y Humanidades5141151Curvature lines on orthogonal surfaces of R3 and Joachimsthal TheoremGeometría diferencialSuperficiesTopologíaTeorema JoachimsthalCurvasprincipal cyclecurvature linesMSC: 53C1234D3053A0537C75http://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/redcol/resource_type/ARTArtículo de revistaORIGINALCurvature lines on orthogonal surfaces.htmlCurvature lines on orthogonal surfaces.htmlartículotext/html239https://repository.usergioarboleda.edu.co/bitstream/11232/310/1/Curvature%20lines%20on%20orthogonal%20surfaces.htmle93129e3e71dc9fc7e05162e0702cfe4MD51open access11232/310oai:repository.usergioarboleda.edu.co:11232/3102021-11-03 15:15:13.711open accessRepositorio Institucional Universidad Sergio Arboledadspace-help@myu.edu
dc.title.spa.fl_str_mv Curvature lines on orthogonal surfaces of R3 and Joachimsthal Theorem
title Curvature lines on orthogonal surfaces of R3 and Joachimsthal Theorem
spellingShingle Curvature lines on orthogonal surfaces of R3 and Joachimsthal Theorem
Geometría diferencial
Superficies
Topología
Teorema Joachimsthal
Curvas
principal cycle
curvature lines
MSC: 53C12
34D30
53A05
37C75
title_short Curvature lines on orthogonal surfaces of R3 and Joachimsthal Theorem
title_full Curvature lines on orthogonal surfaces of R3 and Joachimsthal Theorem
title_fullStr Curvature lines on orthogonal surfaces of R3 and Joachimsthal Theorem
title_full_unstemmed Curvature lines on orthogonal surfaces of R3 and Joachimsthal Theorem
title_sort Curvature lines on orthogonal surfaces of R3 and Joachimsthal Theorem
dc.creator.fl_str_mv Garcia, Ronaldo A.
dc.contributor.author.spa.fl_str_mv Garcia, Ronaldo A.
dc.subject.lemb.spa.fl_str_mv Geometría diferencial
Superficies
Topología
Teorema Joachimsthal
Curvas
topic Geometría diferencial
Superficies
Topología
Teorema Joachimsthal
Curvas
principal cycle
curvature lines
MSC: 53C12
34D30
53A05
37C75
dc.subject.proposal.spa.fl_str_mv principal cycle
curvature lines
MSC: 53C12
34D30
53A05
37C75
description In this paper is studied; as a complement of Joachimsthal theorem; the behavior of curvature lines near a principal cycle common to two orthogonal surfaces.
publishDate 2005
dc.date.issued.spa.fl_str_mv 2005-06-20
dc.date.accessioned.spa.fl_str_mv 2015-07-22T21:13:56Z
2016-05-11T14:34:51Z
2017-05-16T17:17:01Z
dc.date.available.spa.fl_str_mv 2015-07-22T21:13:56Z
2016-05-11T14:34:51Z
2017-05-16T17:17:01Z
dc.date.spa.fl_str_mv 2005
dc.type.coarversion.spa.fl_str_mv http://purl.org/coar/version/c_970fb48d4fbd8a85
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dc.type.local.spa.fl_str_mv Artículo de revista
format http://purl.org/coar/resource_type/c_2df8fbb1
dc.identifier.citation.spa.fl_str_mv Garcia, R. A. (2005). Curvature lines on orthogonal surfaces of R3 and Joachimsthal Theorem. Civilizar Ciencias Sociales y Humanas, 5(8), 141-151.
dc.identifier.issn.spa.fl_str_mv 1657-8953
dc.identifier.doi.eng.fl_str_mv https://doi.org/10.22518/16578953.800
dc.identifier.instname.spa.fl_str_mv instname:Universidad Sergio Arboleda
dc.identifier.reponame.spa.fl_str_mv reponame:Repositorio Institucional Universidad Sergio Arboleda
dc.identifier.repourl.*.fl_str_mv repourl:https://repository.usergioarboleda.edu.co/
dc.identifier.url.eng.fl_str_mv http://hdl.handle.net/11232/310
identifier_str_mv Garcia, R. A. (2005). Curvature lines on orthogonal surfaces of R3 and Joachimsthal Theorem. Civilizar Ciencias Sociales y Humanas, 5(8), 141-151.
1657-8953
instname:Universidad Sergio Arboleda
reponame:Repositorio Institucional Universidad Sergio Arboleda
repourl:https://repository.usergioarboleda.edu.co/
url https://doi.org/10.22518/16578953.800
http://hdl.handle.net/11232/310
dc.language.iso.spa.fl_str_mv spa
language spa
dc.relation.ispartof.spa.fl_str_mv Revista Civilizar Ciencias Sociales y Humanas; vol. 5, núm. 8 (2005)
dc.relation.references.eng.fl_str_mv M. Bergerand B. Gostiaux Introduction to Differential Geometry, Springer Verlag,New York, (1987).
M. do Carmo, Differential Geometry of curves and surfaces, Prentice Hall, New Jersey,(1976).
G. DarbouxLe ̧cons sur la Th ́eorie des Surfaces, vol. I, IV, Gauthiers Villars, (1896).
C. GutierrezandJ. Sotomayor,Closed principal lines and bifurcation, Bull. Braz.Math. Soc.17, 1986, pp. 1-19
R. GarciaandJ. SotomayorLectures Notes on Qualitative Theory of DifferentialEquations of Classical Geometry, Notas de Curso, IME/UFG, (2000).
C. GutierrezandJ. Sotomayor,Lines of Curvature and Umbilic Points on Surfaces,Brazilian 18thMath. Coll., IMPA, 1991, Reprinted asStructurally Configurations ofLines of Curvature and Umbilic Points on Surfaces, Monografias del IMCA, (1998).
H. Hopf,Differential Geometry in the Large, Springer Lecture Notes in Mathematics,vol. 1000, (1983).
D. HilbertandS. Cohn Vossen Geometry and the Imagination, Chelsea, (1952).
M. SpivakA Comprehensive Introduction to Differential Geometry, vol.III, V, Publishof Perish Berkeley, (1979).
M. SpivakA Comprehensive Introduction to Differential Geometry, vol.III, V, Publishof Perish Berkeley, (1979).
dc.relation.references.spa.fl_str_mv A. Gray, L. CordeiroandM. Fernández,Geometría diferencial de curvas y superficies, con Mathematica, Addison-Wesley Iberoamericana, (1995).
dc.relation.references.fre.fl_str_mv G. MongeJourn. de l’Ecole Polytech,IIe, (1796),Applications de l’Algebre a la Geometrie, Paris, (1850).
dc.relation.ispartofjournal.spa.fl_str_mv Civilizar Ciencias Sociales y Humanidades
dc.relation.citationvolumen.spa.fl_str_mv 5
dc.relation.citationstartpage.spa.fl_str_mv 141
dc.relation.citationendpage.spa.fl_str_mv 151
dc.rights.license.*.fl_str_mv Atribución-NoComercial-SinDerivadas 2.5 Colombia (CC BY-NC-ND 2.5 CO)
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dc.rights.acceso.spa.fl_str_mv Abierto (Texto Completo)
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