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It is shown that the generally covariant Duffin-Kemmer-Petiau equation,formulated in the frame of the Tetrode-Weyl-Fock-Ivanenko tetrad formalism,allows for a non-relativistic approximation if the metric tensor is of aspecial form. The Pauli equation for a vector particle involves the Riemanncurvature tensor explicitly. In analogous way, the procedure of thenon-relativistic approximation in the theory of scalar particle, charged andneutral, is investigated in the background of Riemannian space-time. Ageneralized covariant Schrodinger equation is derived when taking into accountnon-minimal interaction term through scalar curvature R(x), it substantiallydiffers from the conventional generally covariant Schrodinger equation producedwhen R(x)=0. It is demonstrated that the the non-relativistic wave function isalways complex-valued irrespective of the type of relativistic scalar particle,charged or neutral, taken initially. The theory of vector particle proves thesame property: even if the wave function of the relativistic particle of spin 1is taken real,the corresponding wave function in the non-relativisticapproximation is complex-valued.

Duffin-Kemmer-Petiau formalism reexamined: non-relativistic approximation for spin 0 and spin 1 particles in a Riemannian space-time