Hyperbolic spaces are of strictly negative type

DOI10.1090/S0002-9939-01-06056-7zbMath0987.32010MaRDI QIDQ2750902

Simon L. Kokkendorff, Poul G. Hjorth, Steen Markvorsen

Publication date: 21 October 2001

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

metric spacesRiemannian manifoldfundamental groupnegative typelength spaces

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) General theory of distance geometry (51K05) Hyperbolic and Kobayashi hyperbolic manifolds (32Q45)

Related Items (16)

Distance geometry in quasihypermetric spaces. III ⋮ Does negative type characterize the round sphere? ⋮ Asymptotic negative type properties of finite ultrametric spaces ⋮ Fractional Brownian fields over manifolds ⋮ ROUNDNESS PROPERTIES OF ULTRAMETRIC SPACES ⋮ Positive definite metric spaces ⋮ Hyperbolic space has strong negative type ⋮ Supremal \(p\)-negative type of vertex transitive graphs ⋮ Strong negative type in spheres ⋮ Enhanced negative type for finite metric trees ⋮ On the supremal \(p\)-negative type of finite metric spaces ⋮ Strict \(p\)-negative type of a metric space ⋮ Characterizing the round sphere by mean distance ⋮ Distance geometry in quasihypermetric spaces. II ⋮ OPTIMAL LOWER BOUND ON THE SUPREMAL STRICT p-NEGATIVE TYPE OF A FINITE METRIC SPACE ⋮ Polygonal equalities and virtual degeneracy in \(L_p\)-spaces

Cites Work

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• Finite metric spaces of strictly negative type
• Distances hilbertiennes invariantes sur un espace homogene

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