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A note on "Sur le noyau de l'operateur de courbure d'une variete finslerienne" [C. R. Acad. Sci. Paris, Ser. A 272 (1971) 807-810]
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A note on "Sur le noyau de l'operateur de courbure d'une variete finslerienne" [C. R. Acad. Sci. Paris, Ser. A 272 (1971) 807-810]

Nabil L. Youssef and Salah G. Elgendi
Comptes rendus. Mathématique, Vol.351(21-22), pp.829-832
01/11/2013
DOI: https://doi.org/10.1016/j.crma.2013.09.025

Abstract

Mathematics Physical Sciences Science & Technology
In this note, adopting the pullback formalism of global Finsler geometry, we show by a counterexample that the kernel Ker(R) of the h-curvature R of the Cartan connection and the associated nullity distribution N-R do not coincide, contrary to a result of Akbar-Zadeh (given in the article that appears in the title). We also give sufficient conditions for KerR and N-R to coincide. (C) 2013 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

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