International Journal of Mathematics and Mathematical Sciences
Volume 31 (2002), Issue 6, Pages 375-379
On hypersurfaces in a locally affine Riemannian Banach manifold
Department of Mathematics, Faculty of Science, Menoufiya University, Menoufiya, 32511, Egypt
Received 12 September 2001
Copyright © 2002 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.
We prove that an essential hypersurface of second order in an
infinite dimensional locally affine Riemannian Banach manifold is
a Riemannian manifold of constant nonzero curvature.