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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)』 ■ウィキペディアで「Hadamard manifold」の詳細全文を読む
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