Hyperbolic spaces are of strictly negative type (Q2750902)
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scientific article; zbMATH DE number 1663147
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Hyperbolic spaces are of strictly negative type |
scientific article; zbMATH DE number 1663147 |
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Hyperbolic spaces are of strictly negative type (English)
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21 October 2001
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Riemannian manifold
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metric spaces
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negative type
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length spaces
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fundamental group
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Finite metric spaces with elements picked from and distances consistent with, embedded in a Riemannian manifold, are studied. The concepts of negative type and strictly negative type are reviewed and the conjecture that hyperbolic spaces are of strictly negative type is settled in the affirmative. The technique of the proof is then applied to show that every compact manifold of negative type must have trivial fundamental group and to obtain a necessary condition for product manifolds to be of negative type.
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