  The roles of crystal-field splitting and Jahn-Teller distortions on the
orbital ordering transition are investigated in the single-layer manganites
near half doping. Crystal-field splitting of energy levels favoring the
$d_{3z^2-r^2}$ occupancy provides not only the correct Fermi surface topology
for La$_{0.5}$Sr$_{1.5}$MnO$_4$ having a circular electron pocket around the
$\Gamma$ point, but also enhances the flatness of the hole pocket around the M
point thereby improving the nesting. In the presence of the circular electron
pocket, Jahn-Teller distortions are found to be crucial for the transition to
the transverse orbital ordering with ordering wavevector ($0.5\pi, 0.5\pi$). In
the hole-doping regime $0.5 \leq x \leq 0.7$, the orbital ordering wavevector
shows a linear dependence on the hole concentration in accordance with the
experiments.
