International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 2, Pages 99-104
doi:10.1155/S0161171204203325
On hypersurfaces in a locally affine Riemannian Banach manifold II
Department of Mathematics, Faculty of Science, Menoufiya University, Menoufiya 32511, Egypt
Received 8 March 2002
Copyright © 2004 El-Said R. Lashin and Tarek F. Mersal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.