On projective transformations of complete Riemannian manifolds with constant scalar curvature (Q2731636)
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scientific article; zbMATH DE number 1626287
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On projective transformations of complete Riemannian manifolds with constant scalar curvature |
scientific article; zbMATH DE number 1626287 |
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12 August 2002
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Riemannian manifold
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projective transformation
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gravitational tensor
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Weyl's projective curvature tensor
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On projective transformations of complete Riemannian manifolds with constant scalar curvature (English)
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The author proves two theorems for a complete and simply connected Riemannian manifold \((M,g)\) of dimension \(n>2\) with a constant scalar curvature \(R\). If there exists a non-affine projective transformation of \((M,g)\) which leaves either the gravitational tensor field (where \(R>0\)) or the covariant derivative of Weyl's projective curvature tensor invariant, then \((M,g)\) is isometric to a Euclidean sphere.
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