  We compute the one-loop potential (the Casimir energy) for scalar, spinor and
vectors fields on the spaces $\,R^{m+1}\, \times\,Y$ with $\,Y=\,S^N\,,CP^2$.
As a physical model we consider spinor electrodynamics on four-dimensional
product manifolds. We examine the cancelation of a divergent part of the
Casimir energy on even-dimensional spaces by means of including the parameter
$\,M$ in original action. For some models we compare our results with those
found in the literature.
