  We develop a variational formulation of a particle with spin in a curved
space-time background. The model is based on a singular Lagrangian which
provides equations of motion, a fixed value of spin and Frenkel condition on
spin-tensor. Comparing our equations with those of Papapetrou we conclude that
the Frenkel electron in a gravitational field has the same behavior as a
rotating body in the pole-dipole and leading-spin approximation. Due to
constraints presented in the formulation, position space is endowed with a
noncommutative structure induced by the spin of the particle. Therefore, the
model provides a physically interesting example of a noncommutative particle in
a curved background.
