  In this paper we study isometric immersions $f:M^n \to {\mathbb
{C}^{\prime}}\!P^n$ of an $n$-dimensional pseudo-Riemannian manifold $M^n$ into
the $n$-dimensional para-complex projective space ${\mathbb
{C}^{\prime}}\!P^n$. We study the immersion $f$ by means of a lift $\mathfrak
f$ of $f$ into a quadric hypersurface in ${S^{2n+1}_{n+1}}$. We find the frame
equations and compatibility conditions. We specialize these results to
dimension $n = 2$ and a definite metric on $M^2$ in isothermal coordinates and
consider the special cases of Lagrangian surface immersions and minimal surface
immersions. We characterize surface immersions with special properties in terms
of primitive harmonicity of the Gauss maps.
