Abstract
it is easily seen that a motion and a homothetic transformation are both affine collineations and that an affine collineation preserves the curvature tensor. In [1 ] one of the present authors proved that in a space of nonzero constant curvature a mapping preserving curvature is a motion. For an Einstein space with nonzero curvature scalar, a mapping preserving Ricci curvature is a motion; for applying the operator L to
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