Manifold with ideal boundaries of different dimensions (Q1412395)
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scientific article; zbMATH DE number 2002268
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Manifold with ideal boundaries of different dimensions |
scientific article; zbMATH DE number 2002268 |
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Manifold with ideal boundaries of different dimensions (English)
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10 November 2003
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\textit{J. Cheeger} and \textit{T. H. Colding} [J. Differ. Geom. 46, No. 3, 406--480 (1997; Zbl 0902.53034)] constructed examples of metrically non-equivalent tangent cones at infinity. All these cones have the same dimension. Moreover, these examples are so-called double warped products. Basing on the methods developed in the above mentioned paper the author constructs in Euclidean space \(\mathbb{R}^8\) a complete metric of nonnegative Ricci curvature having ideal boundaries, and consequently tangent cones at infinity, of different dimensions.
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ideal boundaries
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tangent cone at infinity
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Gromov-Hausdorff limit
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positive Ricci curvature
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double warped product
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