%0 Journal Article
%T Identification of Riemannian foliations on the
tangent bundle via SODE structure
%J Bulletin of the Iranian Mathematical Society
%I Iranian Mathematical Society (IMS)
%Z 1017-060X
%A Laleh, Abolghasem
%A Mir Mohamad Rezaii, Morteza
%A Ahangari, Fateme
%D 2012
%\ 09/15/2012
%V 38
%N 3
%P 669-688
%! Identification of Riemannian foliations on the
tangent bundle via SODE structure
%K Bundle-like metric
%K SODE
%K Semispray
%K Metrizability
%K Riemannian
Foliation
%R
%X The geometry of a system of second order differential equations is the geometry of a semispray, which is a globally defined vector field on TM. The metrizability of a given semispray is of special importance. In this paper, the metric associated with the semispray S is applied in order to study some types of foliations on the tangent bundle which are compatible with SODE structure. Indeed, sufficient conditions for the metric associated with the semispray S are obtained to extend to a bundle-like metric for the lifted foliation on TM. Thus, the lifted foliation converts to a Riemanian foliation on the tangent space which is adapted to the SODE structure. Particularly, the metrizability property of the semispray S is applied in order to induce SODE structure on transversals. Finally, some equivalent conditions are presented for the transversals to be totally geodesic.
%U http://bims.iranjournals.ir/article_232_1c2426a4a61dca0c1d59277a7d46f0c0.pdf