It is proved that any strongly convex Lipschitz differentiable function satisfies the Polyak– Lojasiewicz condition on a proximally smooth C1-smooth manifold under a certain relationship between the proximal smoothness constant of the manifold and strong convexity constant of the function. This condition guarantees a linear convergence rate of the gradient projection method for minimizing the function on the manifold. An algorithm for finding a metric projection of a point located sufficiently close to a manifold onto this manifold is proposed.