Journal of Generalized Lie Theory and Applications


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Here, a Finsler manifold (M,F) is considered with cor-responding curvature tensor, regarded as 2-forms on the bundle of non-zero tangent vectors. Certain subspaces of the tangent spaces of M determined by the curvature are introduced and calledk-nullity foliations of the curvature operator. It is shown that if the dimension of foliation is constant, then the distribution is involutiveand each maximal integral manifold is totally geodesic. Character-ization of the k-nullity foliation is given, as well as some resultsconcerning constancy of the flag curvature, and completeness oftheir integral manifolds, providing completeness of (M,F). Theintroducedk-nullity space is a natural extension of nullity spacein Riemannian geometry, introduced by Chern and Kuiper and en-larged to Finsler setting by Akbar-Zadeh and contains it as a specialcase.


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This article was published in Bulletin of the Iranian Mathematical Society Vol. 37 No. 4, pp 1-18. and referenced in Journal of Generalized Lie Theory and Applications

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