Structure theorems on Riemannian spaces satisfying \(R(X,Y)\cdot R=0\). II. Global versions (Q1088162)

Part I [J. Differ. Geom. 17, 531--582 (1982; Zbl 0508.53025)] gave a local structure theorem for Riemannian spaces satisfying \(R(X,Y)R=0\) (''semisymmetric spaces''). Namely, a dense open subset splits locally as a product of symmetric spaces, surfaces, ''spaces foliated by \(E^{n-2}\)'', ''real cones'', and ''Kaehlerian cones''. In Part I, this last category was characterized only by having \(\nu =2\) and \(n-\nu >2\), where \(\nu\) is is the nullity index of curvature. The present paper completes the classification by finding all metrics which satisfy this condition. A second local factorization theorem is deduced which holds everywhere, not just on a dense subset. Then the significance of completeness for these leaves is studied. The paper culminates in a global structure theorem for \(M\) complete, and a further one for \(M\) complete and analytic.