International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 2, Pages 99-104

On hypersurfaces in a locally affine Riemannian Banach manifold II

El-Said R. Lashin and Tarek F. Mersal

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.


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.