Abstract
A linear complex of lines in the real projective space defines through its focal hyperplanes a totally géodésie distribution of hyperplanes. E. Cartan has shown that conversely, the only non-integrable, totally géodésie distributions of hyperplanes in projective space are of this type. The note gives a new proof of Cartan’s result, based on the notion of totally géodesic quasi-connection.
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References
E. Cartan, Sur un problème de géométrie différentielle projective, Ann. Ec. Norm. 62(1945).
T. Hangan, R. Lutz, Champs d’hyperplans totalement géodésiques sur les sphères, Soc. Math. France, Asterisque 107–108(1983), 189–200.
T. Hangan, On Totally Geodesic Distribution of Planes, Coll. Math. Soc. János Bolyai, 46, Debrecen 1984.
T. Hangan, Sur les distribution de plans totalement géodésiques, Publicationes de la Universidad de Murcia, 1983.
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© 1998 Springer Science+Business Media Dordrecht
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Hangan, T. (1998). Sur Un Probleme D’Elie Cartan. In: Khakimdjanov, Y., Goze, M., Ayupov, S.A. (eds) Algebra and Operator Theory. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5072-9_14
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DOI: https://doi.org/10.1007/978-94-011-5072-9_14
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