超球面

在高维几何中,超球面(英語:Hypersphere)是指高維空間中,和一定点(称为中心)距離(称为半徑)為定值的點組成的集合。超球面是餘維數為1的流形,其維數比其空間維數少一。超球面的半徑越大,其曲率越小。若曲率趨近於0,稱為超平面。超球面和超平面都屬於超曲面

超球面(hypersphere)一詞是由Duncan Sommerville英语Duncan Sommerville在討論非歐氏幾何學的模型時出現的[1],第一個提的是四維空間中的三維球面

有些球面不是超球面,若SEm的球體,而所在空間為nm < n,則S不是超球面。同樣的,任何空間內flat內的N维球面也不會是超球面,例如在三維空間中,圓不是超球面,但在二維空間中就是超球面。

参考文献

  1. ^ D. M. Y. Sommerville (1914) The Elements of Non-Euclidean Geometry页面存档备份,存于互联网档案馆), p. 193, link from University of Michigan Historical Math Collection

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