On hypersurfaces in a locally affine Riemannian Banach manifold II
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 constan...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204203325 |
| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |