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On the Existence of a Codimension 1 Completely Integrable Totally Geodesic Distribution on a Pseudo-Riemannian Heisenberg Group

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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Main Authors: Batat, W., Rahmani, S.
Format: Article
Language:English
Published: Інститут математики НАН України 2010
Series:Symmetry, Integrability and Geometry: Methods and Applications
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/146314
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spelling irk-123456789-1463142019-02-09T01:24:43Z On the Existence of a Codimension 1 Completely Integrable Totally Geodesic Distribution on a Pseudo-Riemannian Heisenberg Group Batat, W. Rahmani, S. 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. 2010 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/146314 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
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.
format Article
author Batat, W.
Rahmani, S.
spellingShingle Batat, W.
Rahmani, S.
On the Existence of a Codimension 1 Completely Integrable Totally Geodesic Distribution on a Pseudo-Riemannian Heisenberg Group
Symmetry, Integrability and Geometry: Methods and Applications
author_facet Batat, W.
Rahmani, S.
author_sort Batat, W.
title 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_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_sort on the existence of a codimension 1 completely integrable totally geodesic distribution on a pseudo-riemannian heisenberg group
publisher Інститут математики НАН України
publishDate 2010
url http://dspace.nbuv.gov.ua/handle/123456789/146314
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.
series Symmetry, Integrability and Geometry: Methods and Applications
work_keys_str_mv AT batatw ontheexistenceofacodimension1completelyintegrabletotallygeodesicdistributiononapseudoriemannianheisenberggroup
AT rahmanis ontheexistenceofacodimension1completelyintegrabletotallygeodesicdistributiononapseudoriemannianheisenberggroup
first_indexed 2023-05-20T17:24:05Z
last_indexed 2023-05-20T17:24:05Z
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