  The optimal target dimensions are determined for totally real immersions and
for independent mappings into complex affine spaces. Our arguments are similar
to those given by Forster, but we use orientable manifolds as far as possible
and so are able to obtain improved results for orientable manifolds of even
dimension. This leads to new examples showing that the known immersion and
submersion dimensions for holomorphic mappings from Stein manifolds to affine
spaces are best possible.
