Obstruction to prescribed positive Ricci curvature (Q1122794)

This paper extends to non-compact manifolds the obstruction results of \textit{D. DeTurck} and \textit{N. Koiso} [Ann. Inst. Henri Poincaré, Anal. Non Linéaire 1, 351-359 (1984; Zbl 0556.53026)]. The main result states that a Riemannian metric, with largest eigenvalue of the curvature operator uniformly strictly less than 1, cannot be realized as the Ricci tensor of a complete metric. Calabi's maximum principle [\textit{E. Calabi}, Duke Math. J. 25, 45-56 (1958; Zbl 0079.118)] is a key-tool of the proof.