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We prove a global continuation result for $T$-periodic solutions of a$T$-periodic parametrized second order retarded functional differentialequation on a boundaryless compact manifold with nonzero Euler-Poincare'characteristic. The approach is based on the fixed point index theory forlocally compact maps on ANRs. As an application, we prove the existence offorced oscillations of retarded functional motion equations defined ontopologically nontrivial compact constraints. This existence result is obtainedunder the assumption that the frictional coefficient is nonzero, and weconjecture that it is still true in the frictionless case.

A continuation result for forced oscillations of constrained motion problems with infinite delay