On hypersurfaces in a locally affine Riemannian Banach manifold. II (Q1774646)

Summary: In our previous work [ibid. 31, No. 6, 275--379 (2002; Zbl 1021.53031)], we proved that an essential second-order hypersurface in an infinite-dimensional locally affine Riemannian Banach manifold is a Riemannian manifold of constant nonzero curvature. In this note, we prove the converse, in other words, we prove that a hypersurface of constant nonzero Riemannian curvature in a locally affine (flat) semi-Riemannian Banach space is an essential hypersurface of second order.