  We propose a special deformation of the Sasaki metric on tangent and unit
tangent bundle of a Hermitian locally symmetric manifold. Geodesics of this
deformed metric have different projections on a base manifold for tangent or
unit tangent bundle cases in contrast to usual Sasaki metric. Nevertheless, the
projections of geodesics of the unit tangent bundle still preserve the property
to have all geodesic curvatures constant.
