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International Journal of Mathematics and Mathematical Sciences
Volume 31, 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 Hindawi Publishing Corporation. 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.