  In this paper, we give the geometric meaning of hypersurfaces with constant
mean curvature in a Finsler manifold by using volume preserving variation. Then
we give the correspondence between principal curvatures of submanifolds by a
homothetic navigation, which means that some geometric properties of
submanifolds are the same. Finally, we deduce a Heintze-Karcher type inequality
and prove an Alexandrov type theorem in special Finsler spaces.
