  In this paper, we extend the mimetic gravity to the multi-field setup with a
curved field space manifold. The multi-field mimetic scenario is realized via
the singular limit of the conformal transformation between the auxiliary and
the physical metrics. We look for the cosmological implications of the setup
where it is shown that at the background level the mimetic energy density
mimics the roles of dark matter. At the perturbation level, the scalar field
perturbations are decomposed into the tangential and normal components with
respect to the background field space trajectory. The adiabatic perturbation
tangential to the background trajectory is frozen while the entropy mode
perpendicular to the background trajectory propagates with the speed of unity.
Whether or not the entropy perturbation is healthy directly depends on the
signature of the field-space metric. We perform the full non-linear Hamiltonian
analysis of the system with the curved field space manifold and calculate the
physical degrees of freedom verifying that the system is free from the
Ostrogradsky-type ghost.
