On hypersurfaces in a locally affine Riemannian Banach manifold (Q1607959)
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scientific article; zbMATH DE number 1780434
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On hypersurfaces in a locally affine Riemannian Banach manifold |
scientific article; zbMATH DE number 1780434 |
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On hypersurfaces in a locally affine Riemannian Banach manifold (English)
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13 August 2002
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An essential hypersurface of order two is one whose elements \(X\) comply with an equation \(g(X,X)=er^2\) (\(e\) being equal to \(-1,0\), or \(+1\), \(r\) being an arbitrary nonzero real number) with respect to the first differential form \(g\). The authors prove the following theorem: An essential hypersurface of order two in an infinite-dimensional locally Riemannian Banach manifold is a Riemannian manifold of constant nonzero curvature.
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Riemannian manifold
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Banach manifold
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