Mathematics – Differential Geometry
Scientific paper
2008-05-16
Int.J.Geom.Meth.Mod.Phys.6:1003-1031,2009
Mathematics
Differential Geometry
27 pages, LaTex file, Some typographical errors corrected, Some formulas simpified
Scientific paper
10.1142/S0219887809003904
The present paper deals with an \emph{intrinsic} investigation of the notion of a concurrent $\pi$-vector field on the pullback bundle of a Finsler manifold $(M,L)$. The effect of the existence of a concurrent $\pi$-vector field on some important special Finsler spaces is studied. An intrinsic investigation of a particular $\beta$-change, namely the energy $\beta$-change ($\widetilde{L}^{2}(x,y)=L^{2}(x,y)+ B^{2}(x,y) with \ B:=g(\bar{\zeta},\bar{\eta})$; $\bar{\zeta} $ being a concurrent $\pi$-vector field), is established. The relation between the two Barthel connections $\Gamma$ and $\widetilde{\Gamma}$, corresponding to this change, is found. This relation, together with the fact that the Cartan and the Barthel connections have the same horizontal and vertical projectors, enable us to study the energy $\beta$-change of the fundamental linear connection in Finsler geometry: the Cartan connection, the Berwald connection, the Chern connection and the Hashiguchi connection. Moreover, the change of their curvature tensors is concluded. It should be pointed out that the present work is formulated in a prospective modern coordinate-free form.
Abed S. H.
Soleiman A.
Youssef Nabil L.
No associations
LandOfFree
Concurrent $π$-vector fields and energy beta-change does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Concurrent $π$-vector fields and energy beta-change, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Concurrent $π$-vector fields and energy beta-change will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-273573