Conic–connected manifolds

We study a particular class of rationally connected manifolds, X HPN, such that two general points x;x0 A X may be joined by a conic contained in X. We prove that these manifolds are Fano, with b2 e 2. Moreover, a precise classification is obtained for b2 1⁄4 2. Complete intersections of high dimension with respect to their multi-degree provide examples for the case b2 1⁄4 1. The proof of the classification result uses a general characterization of rationality, in terms of suitable covering families of rational curves.