Hypersurfaces of the spherical type degenerated
In this work, we define the hypersurfaces of the spherical type degenerated (in short DST-hypersurfaces), these hypersurfaces has the geometric property that the middle spheres pass through the origin of the Euclidean space. We present a representation for these hypersurfaces in the case where the s...
| Main Authors: | , , |
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| Format: | Article |
| Language: | Spanish |
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Universidad Nacional de Trujillo
2020-12-01
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| Series: | Selecciones Matemáticas |
| Subjects: | |
| Online Access: | https://revistas.unitru.edu.pe/index.php/SSMM/article/view/3111 |
| _version_ | 1818871870730010624 |
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| author | Armando M. V. Corro Diogo G. Dias Carlos M. C. Riveros |
| author_facet | Armando M. V. Corro Diogo G. Dias Carlos M. C. Riveros |
| author_sort | Armando M. V. Corro |
| collection | DOAJ |
| description | In this work, we define the hypersurfaces of the spherical type degenerated (in short DST-hypersurfaces), these hypersurfaces has the geometric property that the middle spheres pass through the origin of the Euclidean space. We present a representation for these hypersurfaces in the case where the stereographic projection of the Gauss map N is given by the identity application. We characterize the DST-hypersurfaces through a differential equation and we give an explicit example of a two-parameter family of DST-hypersurfaces with planar lines of curvature foliated by (n-1)-dimensional spheres. Moreover, we classify the DST hypersurfaces of rotation. |
| first_indexed | 2024-12-19T12:29:47Z |
| format | Article |
| id | doaj.art-becc58ff3e5b4fbaabb5caf788be9852 |
| institution | Directory Open Access Journal |
| issn | 2411-1783 2411-1783 |
| language | Spanish |
| last_indexed | 2024-12-19T12:29:47Z |
| publishDate | 2020-12-01 |
| publisher | Universidad Nacional de Trujillo |
| record_format | Article |
| series | Selecciones Matemáticas |
| spelling | doaj.art-becc58ff3e5b4fbaabb5caf788be98522022-12-21T20:21:27ZspaUniversidad Nacional de TrujilloSelecciones Matemáticas2411-17832411-17832020-12-0170221422110.17268/sel.mat.2020.02.03Hypersurfaces of the spherical type degeneratedArmando M. V. Corro0https://orcid.org/0000-0002-6864-3876Diogo G. Dias1https://orcid.org/0000-0001-5236-0057Carlos M. C. Riveros2https://orcid.org/0000-0002-1206-7072Instituto de Matemática e Estatística, Universidade Federal de Goias, 74001-970, Goiania-GO, Brazil.Instituto Federal de Educacao Ciencia e Tecnologia de Goias, Aparecida de Goiania, 74968-755, GO, Brazil.Departamento de Matemática,Universidade de Brasília, 70910-900, Brasília-DF, BrazilIn this work, we define the hypersurfaces of the spherical type degenerated (in short DST-hypersurfaces), these hypersurfaces has the geometric property that the middle spheres pass through the origin of the Euclidean space. We present a representation for these hypersurfaces in the case where the stereographic projection of the Gauss map N is given by the identity application. We characterize the DST-hypersurfaces through a differential equation and we give an explicit example of a two-parameter family of DST-hypersurfaces with planar lines of curvature foliated by (n-1)-dimensional spheres. Moreover, we classify the DST hypersurfaces of rotation.https://revistas.unitru.edu.pe/index.php/SSMM/article/view/3111edsgw-surfacessurfaces of the spherical typesupport functionplanar lines of curvature |
| spellingShingle | Armando M. V. Corro Diogo G. Dias Carlos M. C. Riveros Hypersurfaces of the spherical type degenerated Selecciones Matemáticas edsgw-surfaces surfaces of the spherical type support function planar lines of curvature |
| title | Hypersurfaces of the spherical type degenerated |
| title_full | Hypersurfaces of the spherical type degenerated |
| title_fullStr | Hypersurfaces of the spherical type degenerated |
| title_full_unstemmed | Hypersurfaces of the spherical type degenerated |
| title_short | Hypersurfaces of the spherical type degenerated |
| title_sort | hypersurfaces of the spherical type degenerated |
| topic | edsgw-surfaces surfaces of the spherical type support function planar lines of curvature |
| url | https://revistas.unitru.edu.pe/index.php/SSMM/article/view/3111 |
| work_keys_str_mv | AT armandomvcorro hypersurfacesofthesphericaltypedegenerated AT diogogdias hypersurfacesofthesphericaltypedegenerated AT carlosmcriveros hypersurfacesofthesphericaltypedegenerated |