International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 2, Pages 99-104
doi:10.1155/S0161171204203325
Abstract
In our previous work (2002), 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.