Journal ArticleDOI
A Remarkable property of the Riemann-Christoffel tensor in four dimensions
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In this paper, it was shown that two invariants are inactive in the formation of field equations and thus may be omitted from the integrand of the action principle, i.e., I, = Ra, 6Ra# and 12 = R2.Abstract:
Introduction. If the geometry of nature is Riemannian and the field equations of this geometry are controlled by a scale-invariant action principle, there are four a priori possible and algebraically independent invariants which may enter in the integrand of the action principle. This abundance of invariants hampers the mathematical development and the logical appeal of the theory. The present paper shows that two of these invariants are inactive in the formation of field equations and thus may be omitted. Only the two invariants I, = Ra,6Ra# and 12 =R2read more
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