A RIGIDITY THEOREM FOR SIMPLY CONNECTED MANIFOLDS WITHOUT CONJUGATE-POINTS

In this paper we show that manifolds without conjugate points exhibit rigidity phenomena similar to that studied in [BGS, Section I.5]. The main theorem is that if X is a complete, simply connected Riemannian m anifold without conjugate points, and M = X x R is given the Riemannia n product metric g, then any metric without conjugate points on M whic h agrees with g outside a compact set is isometric to g.