volume 31, issue 4, P515-543 2004
DOI: 10.1007/s00454-004-0806-2
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Abstract: We develop the utility of Gram matrix machinery as a tool to treat the geometry of simplices in space forms. A formula relating the determinant of a normalized Gram matrix to the geometry of the simplex it represents is presented. We then apply the tools to leaf spaces, i.e. the set of degree 1 vertices of a metric tree. One main result is that for a given metric space X there exists a constant κ 0 < 0, such that X embeds into all hyperbolic spaces of curvature less than κ 0 , if and only if X is a leaf space…

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