  We study the connection between a multitime scalar variational problem (SVP),
a multitime vector variational problem (VVP) and a multitime vector fractional
variational problem (VFP). For (SVP), we establish necessary optimality
conditions. For both vector variational problems, we define the notions of
Pareto efficient solution and of normal efficient solution and we establish
necessary efficiency conditions for (VVP) and (VFP) using both notions. The
main purpose of the paper is to establish sufficient efficiency conditions for
the vector problems (VVP) and (VFP). Moreover, we obtain sufficient optimality
conditions for (SVP). The sufficient conditions are based on our original
notion of $(\rho ,b)$-geodesic quasiinvexity.
