  We study a class of D=11 BPS spacetimes that describe M-branes wrapping
supersymmetric 2 and 4-cycles of Calabi-Yau 3-folds. We analyze the geometrical
significance of the supersymmetry constraints and gauge field equations of
motion for these spacetimes. We show that the dimensional reduction to D=5
yields known BPS black hole and black string solutions of D=5, N=2
supergravity. The usual ansatz for the dimensional reduction is valid only in
the linearized regime of slowly varying moduli and small gauge field strengths.
Our identification of the massless D=5 modes with D=11 quantities extends
beyond this regime and should prove useful in constructing non-linear ansatze
for Calabi-Yau dimensional reductions of supergravity theories.
