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Mehdi Rafie-Rad

Mehdi Rafie-Rad

Academic rank: Associate Professor
ORCID: 0000-0002-8214-3835
Education: PhD.
ScopusId: 23493274700
Faculty: Faculty of Mathematical Sciences
Address:
Phone: 01135302464

Research

Title
On the k-nullity foliations in Finsler geometry
Type
JournalPaper
Keywords
Foliation, k-nullity, Finsler manifolds, curvature operator
Year
2011
Journal Bulletin of the Iranian Mathematical Society
DOI
Researchers Mehdi Rafie-Rad ، Behroz Bidabad

Abstract

Here, a Finsler manifold (M, F) is considered with corresponding 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 called knullity foliations of the curvature operator. It is shown that if the dimension of foliation is constant, then the distribution is involutive and each maximal integral manifold is totally geodesic. Characterization of the k-nullity foliation is given, as well as some results concerning constancy of the flag curvature, and completeness of their integral manifolds, providing completeness of (M, F). The introduced k-nullity space is a natural extension of nullity space in Riemannian geometry, introduced by Chern and Kuiper and enlarged to Finsler setting by Akbar-Zadeh and contains it as a special case.