Rigid manifolds of general type with non-contractible universal cover

For each n≥3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n\ge 3$$\end{document} we give examples of infinitesimally rigid projective manifolds of general type of dimension n with non-contractible universal cover. We provide examples with projective and examples with non-projective universal cover.