Abstract
On a previous occasion it was shown that the « natural generalization » to a Riemann spaceV 4 of a certain set of flat-space free-field equations for particles of spinS=3/2 is internally consistent if and only if theV 4 is an Einstein space. It is now shown that, this case apart, all equations for particles of spinS⩾3/2 which may be said to conform to a « strong principle of equivalence » are compatible if and only if theV 4 is of constant Riemannian curvature. The corresponding second-order wave equations in such a space are written down. Certain modified first-order equations for the caseS=2 which involve the curvature tensor explicitly are shown to be consistent in an Einstein space.
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