  The main two families of real hypersurfaces in complex space forms are Hopf
and ruled. However, very little is known about real hypersurfaces in the
indefinite complex projective space $\cpn$. In a previous work, Kimura and the
second author introduced Hopf real hypersurfaces in $\cpn$. In this paper,
ruled real hypersurfaces in the indefinite complex projective space are
introduced, as those whose maximal holomorphic distribution is integrable, and
such that the leaves are totally geodesic holomorphic hyperplanes. A detailed
description of the shape operator is computed, obtaining two main different
families. A method of construction is exhibited, by gluing in a suitable way
totally geodesic holomorphic hyperplanes along a non-null curve. Next, the
classification of all minimal ruled real hypersurfaces is obtained, in terms of
three main families of curves, namely geodesics, totally real circles and a
third case which is not a Frenet curve, but can be explicitly computed. Four
examples of minimal ruled real hypersurfaces are described.
