An examination of the rotation and Fermi-rotation tensors of an arbitrary C vector field. The Fermi-rotation tensor is shown to be the natural generalization of the classic concept of a rotation tensor, and conditions are obtained under which the usually encountered rotation tensor gives the same measure as the Fermi tensor. The two are equivalent if and only if the motion generated by the vector field is geodesic in conformally related space-time. Explicit characterizations of irrotational and Fermi-irrotational motions are obtained. Necessary and sufficient conditions are derived for an Einstein-Riemann space to admit such motions
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