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On the Existence of a Codimension 1 Completely Integrable Totally Geodesic Distribution on a Pseudo-Riemannian Heisenberg Group
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2010, том 6
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On the Existence of a Codimension 1 Completely Integrable Totally Geodesic Distribution on a Pseudo-Riemannian Heisenberg Group
Інший ID:
2010 Mathematics Subject Classification: 58A30; 53C15; 53C30
DOI:10.3842/SIGMA.2010.021
DOI:10.3842/SIGMA.2010.021
Посилання:
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.
Підтримка:
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.
Дата:
2010
Переглядів:
531
Завантажень:
247
Анотація:
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.
