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A new mechanism is proposed for generating neutrino masses radiativelythrough a non-minimal coupling to gravity of fermionic bilinears involvingmassive neutral fermions. Such coupling terms can arise in theories where thegravity sector is augmented by a scalar field. They necessarily violate theprinciple of equivalence, but such violations are not ruled out by presentexperiments. It is shown that the proposed mechanism is realised mostconvincingly in theories of the Randall- Sundrum type, where gravity couplesstrongly in the TeV range. The mechanism has the potential for solving both thesolar and atmospheric neutrino problems. The smallness of neutrino masses inthis scenario is due to the fact that the interaction of the massive neutralfermions arises entirely from higher-dimensional operators in the effectiveLagrangian.Comment: 7 page Latex 2e file, axodraw needed. Discussion and references  added. Version to appear in MPL

NEUTRINO MASSES FROM NON-MINIMAL GRAVITATIONAL INTERACTIONS OF MASSIVE NEUTRAL FERMIONS