  Based on the Hamiltonian of small polarons with the strong nearest neighbor
repulsion, we have investigated the charge ordering phenomena observed in
half-doped manganites R_{1/2}A_{1/2}MnO_3. We have explored possible
consequences of the charge ordering phase in the half-doped manganites. First,
we have studied the renormalization of the sound velocity around $T_{CO}$,
considering the acoustic phonons coupled to the electrons participating in the
charge ordering. Second, we have found a new antiferromagnetic phase induced by
the charge ordering, and discussed its role in connection with the specific
CE-type antiferromagnetic structure observed in half-doped manganites.
