TY - JOUR
ID - 367
TI - On the k-nullity foliations in Finsler geometry
JO - Bulletin of the Iranian Mathematical Society
JA - BIMS
LA - en
SN - 1017-060X
AU - Bidabad, B.
AU - Rafie-Rad, M.
AD -
Y1 - 2011
PY - 2011
VL - 37
IS - No. 4
SP - 1
EP - 18
KW - Foliation
KW - k-nullity
KW - Finsler manifolds
KW - curvature operator
DO -
N2 - 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 $k$-nullity 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.
UR - http://bims.iranjournals.ir/article_367.html
L1 - http://bims.iranjournals.ir/article_367_fb2ca9742a5a21adfec049f51eb72767.pdf
ER -