On the Existence of a Codimension 1 Completely Integrable Totally Geodesic Distribution on a Pseudo-Riemannian Heisenberg Group
In this note we prove that the Heisenberg group with a left-invariant pseudo-Riemannian metric admits a completely integrable totally geodesic distribution of codimension 1. This is on the contrary to the Riemannian case, as it was proved by T. Hangan.
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2010 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2010
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146314 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | On the Existence of a Codimension 1 Completely Integrable Totally Geodesic Distribution on a Pseudo-Riemannian Heisenberg Group / W. Batat, S. Rahmani // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 9 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862583716283416576 |
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| author | Batat, W. Rahmani, S. |
| author_facet | Batat, W. Rahmani, S. |
| citation_txt | On the Existence of a Codimension 1 Completely Integrable Totally Geodesic Distribution on a Pseudo-Riemannian Heisenberg Group / W. Batat, S. Rahmani // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 9 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In this note we prove that the Heisenberg group with a left-invariant pseudo-Riemannian metric admits a completely integrable totally geodesic distribution of codimension 1. This is on the contrary to the Riemannian case, as it was proved by T. Hangan.
|
| first_indexed | 2025-11-27T00:42:54Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146314 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-27T00:42:54Z |
| publishDate | 2010 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Batat, W. Rahmani, S. 2019-02-08T20:30:32Z 2019-02-08T20:30:32Z 2010 On the Existence of a Codimension 1 Completely Integrable Totally Geodesic Distribution on a Pseudo-Riemannian Heisenberg Group / W. Batat, S. Rahmani // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 9 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 58A30; 53C15; 53C30 DOI:10.3842/SIGMA.2010.021 https://nasplib.isofts.kiev.ua/handle/123456789/146314 In this note we prove that the Heisenberg group with a left-invariant pseudo-Riemannian metric admits a completely integrable totally geodesic distribution of codimension 1. This is on the contrary to the Riemannian case, as it was proved by T. Hangan. The authors wish to express their gratitude toward the referees for their valuable remarks and also would like to thank Professor Jos´e Antonio Oubi˜na for his fruitful comments on the revised version of this paper. The first author was supported by ENSET d’Oran and the second author is indebted to Doctoral School of Dynamical Systems and Geometry (U.S.T. Oran) for its financial support during the elaboration of this work. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On the Existence of a Codimension 1 Completely Integrable Totally Geodesic Distribution on a Pseudo-Riemannian Heisenberg Group Article published earlier |
| spellingShingle | On the Existence of a Codimension 1 Completely Integrable Totally Geodesic Distribution on a Pseudo-Riemannian Heisenberg Group Batat, W. Rahmani, S. |
| title | On the Existence of a Codimension 1 Completely Integrable Totally Geodesic Distribution on a Pseudo-Riemannian Heisenberg Group |
| title_full | On the Existence of a Codimension 1 Completely Integrable Totally Geodesic Distribution on a Pseudo-Riemannian Heisenberg Group |
| title_fullStr | On the Existence of a Codimension 1 Completely Integrable Totally Geodesic Distribution on a Pseudo-Riemannian Heisenberg Group |
| title_full_unstemmed | On the Existence of a Codimension 1 Completely Integrable Totally Geodesic Distribution on a Pseudo-Riemannian Heisenberg Group |
| title_short | On the Existence of a Codimension 1 Completely Integrable Totally Geodesic Distribution on a Pseudo-Riemannian Heisenberg Group |
| title_sort | on the existence of a codimension 1 completely integrable totally geodesic distribution on a pseudo-riemannian heisenberg group |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146314 |
| work_keys_str_mv | AT batatw ontheexistenceofacodimension1completelyintegrabletotallygeodesicdistributiononapseudoriemannianheisenberggroup AT rahmanis ontheexistenceofacodimension1completelyintegrabletotallygeodesicdistributiononapseudoriemannianheisenberggroup |