On hypersurfaces in a locally affine Riemannian Banach manifold II

El-Said R. Lashin and Tarek F. Mersal

International Journal of Mathematics and Mathematical Sciences, 2004, vol. 2004, 1-6

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.

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:497269

DOI: 10.1155/S0161171204203325

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