TY - JOUR
ID - 232
TI - Identification of Riemannian foliations on the
tangent bundle via SODE structure
JO - Bulletin of the Iranian Mathematical Society
JA - BIMS
LA - en
SN - 1017-060X
AU - Laleh, Abolghasem
AU - Mir Mohamad Rezaii, Morteza
AU - Ahangari, Fateme
AD - Amirkabir University of Technology
Y1 - 2012
PY - 2012
VL - 38
IS - 3
SP - 669
EP - 688
KW - Bundle-like metric
KW - SODE
KW - Semispray
KW - Metrizability
KW - Riemannian
Foliation
DO -
N2 - 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.
UR - http://bims.iranjournals.ir/article_232.html
L1 - http://bims.iranjournals.ir/article_232_1c2426a4a61dca0c1d59277a7d46f0c0.pdf
ER -