A note on "Sur le noyau de l'opérateur de courbure d'une variété finslérienne" [C. R. Acad. Sci. Paris, t. 272 (1971), 807-810]

Abstract

In this note, adopting the pullback formalism of global Finsler geometry, we show by a counterexample that the kernel ${\text{Ker}}_R$ of the h-curvature $R$ of Cartan connection and the associated nullity distribution ${\mathbb{N}}_R$ do not coincide, contrary to Akbar-Zadeh's result \cite{akbar.nul3.}. We give sufficient conditions for ${\text{Ker}}_R$ and ${\mathbb{N}}_R$ to coincide.

4 pages, LaTeX file, small correction in the counterexample. Some modifications have been performed especially at the end of the paper

References in corpus (3)

• Geometric objects associated with the fundamental connections in Finsler geometry
• On k-nullity foliations in Finsler geometry and completeness
• On Akbar-Zadeh's Theorem on a Finsler Space of Constant Curvature