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...
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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 |
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doaj-335fd8f3604148048b9ce684ebdaeceb2020-11-24T22:55:57ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-01200429910410.1155/S0161171204203325On hypersurfaces in a locally affine Riemannian Banach manifold IIEl-Said R. Lashin0Tarek F. Mersal1Department of Mathematics, Faculty of Science, Menoufiya University, Menoufiya 32511, EgyptDepartment of Mathematics, Faculty of Science, Menoufiya University, Menoufiya 32511, EgyptIn 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.http://dx.doi.org/10.1155/S0161171204203325 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
El-Said R. Lashin Tarek F. Mersal |
| spellingShingle |
El-Said R. Lashin Tarek F. Mersal On hypersurfaces in a locally affine Riemannian Banach manifold II International Journal of Mathematics and Mathematical Sciences |
| author_facet |
El-Said R. Lashin Tarek F. Mersal |
| author_sort |
El-Said R. Lashin |
| title |
On hypersurfaces in a locally affine Riemannian Banach manifold II |
| title_short |
On hypersurfaces in a locally affine Riemannian Banach manifold II |
| title_full |
On hypersurfaces in a locally affine Riemannian Banach manifold II |
| title_fullStr |
On hypersurfaces in a locally affine Riemannian Banach manifold II |
| title_full_unstemmed |
On hypersurfaces in a locally affine Riemannian Banach manifold II |
| title_sort |
on hypersurfaces in a locally affine riemannian banach manifold ii |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2004-01-01 |
| description |
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. |
| url |
http://dx.doi.org/10.1155/S0161171204203325 |
| work_keys_str_mv |
AT elsaidrlashin onhypersurfacesinalocallyaffineriemannianbanachmanifoldii AT tarekfmersal onhypersurfacesinalocallyaffineriemannianbanachmanifoldii |
| _version_ |
1725655647283838976 |