A Discrete Representation of the Second Fundamental Form
We present a new method to obtain a combinatorial representation for the behaviour of a submanifold isometrically immersed in a Riemannian manifold based on the second fundamental form. We also present several results applying this new way of representation.
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-06-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/10/13/2279 |
| _version_ | 1827598891081531392 |
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| author | Alfonso Carriazo Luis M. Fernández Antonio Ramírez-de-Arellano |
| author_facet | Alfonso Carriazo Luis M. Fernández Antonio Ramírez-de-Arellano |
| author_sort | Alfonso Carriazo |
| collection | DOAJ |
| description | We present a new method to obtain a combinatorial representation for the behaviour of a submanifold isometrically immersed in a Riemannian manifold based on the second fundamental form. We also present several results applying this new way of representation. |
| first_indexed | 2024-03-09T04:01:23Z |
| format | Article |
| id | doaj.art-4c20fe6cb92f4e1cb94c0f6bee0f1afe |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T04:01:23Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-4c20fe6cb92f4e1cb94c0f6bee0f1afe2023-12-03T14:12:09ZengMDPI AGMathematics2227-73902022-06-011013227910.3390/math10132279A Discrete Representation of the Second Fundamental FormAlfonso Carriazo0Luis M. Fernández1Antonio Ramírez-de-Arellano2Departamento de Geometría y Topología, Facultad de Matemáticas, Universidad de Sevilla, C./Tarfia, s.n., 41012 Sevilla, SpainDepartamento de Geometría y Topología, Facultad de Matemáticas, Universidad de Sevilla, C./Tarfia, s.n., 41012 Sevilla, SpainDepartamento de Geometría y Topología, Facultad de Matemáticas, Universidad de Sevilla, C./Tarfia, s.n., 41012 Sevilla, SpainWe present a new method to obtain a combinatorial representation for the behaviour of a submanifold isometrically immersed in a Riemannian manifold based on the second fundamental form. We also present several results applying this new way of representation.https://www.mdpi.com/2227-7390/10/13/2279geometry of submanifoldscombinatorial structuresecond fundamental formtotally umbilical submanifoldminimal submanifoldLagrangian submanifold |
| spellingShingle | Alfonso Carriazo Luis M. Fernández Antonio Ramírez-de-Arellano A Discrete Representation of the Second Fundamental Form Mathematics geometry of submanifolds combinatorial structure second fundamental form totally umbilical submanifold minimal submanifold Lagrangian submanifold |
| title | A Discrete Representation of the Second Fundamental Form |
| title_full | A Discrete Representation of the Second Fundamental Form |
| title_fullStr | A Discrete Representation of the Second Fundamental Form |
| title_full_unstemmed | A Discrete Representation of the Second Fundamental Form |
| title_short | A Discrete Representation of the Second Fundamental Form |
| title_sort | discrete representation of the second fundamental form |
| topic | geometry of submanifolds combinatorial structure second fundamental form totally umbilical submanifold minimal submanifold Lagrangian submanifold |
| url | https://www.mdpi.com/2227-7390/10/13/2279 |
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