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Hadamard manifold : ウィキペディア英語版
Hadamard manifold
In mathematics, a Hadamard manifold, named after Jacques Hadamard — sometimes called a Cartan–Hadamard manifold, after Élie Cartan — is a Riemannian manifold (''M'', ''g'') that is complete and simply-connected, and has everywhere non-positive sectional curvature.
==Examples==

* The real line R with its usual metric is a Hadamard manifold with constant sectional curvature equal to 0.
* Standard ''n''-dimensional hyperbolic space H''n'' is a Hadamard manifold with constant sectional curvature equal to −1.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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