  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 a
special form. The Pauli equation for a vector particle involves the Riemann
curvature tensor explicitly. In analogous way, the procedure of the
non-relativistic approximation in the theory of scalar particle, charged and
neutral, is investigated in the background of Riemannian space-time. A
generalized covariant Schrodinger equation is derived when taking into account
non-minimal interaction term through scalar curvature R(x), it substantially
differs from the conventional generally covariant Schrodinger equation produced
when R(x)=0. It is demonstrated that the the non-relativistic wave function is
always complex-valued irrespective of the type of relativistic scalar particle,
charged or neutral, taken initially. The theory of vector particle proves the
same property: even if the wave function of the relativistic particle of spin 1
is taken real,the corresponding wave function in the non-relativistic
approximation is complex-valued.
