论黎曼流形与外尔流形之区别
首发时间:2009-11-17
摘要:外尔流形与黎曼流形是两个不同的流形概念。但在许多文献中没有将外尔流形与黎曼流形明确的区分开,而是往往将二者混淆,要么是将外尔流形定义内容当成是黎曼流形定义内容,要么是将外尔流形与黎曼流形混为一谈,要么是将外尔流形定义看成是对黎曼流形的“清晰的数学描述”,等等。针对各种错误观点,本文作了如下创新工作: a). 本文从流形的定义、流形的数学思想、流形的数学方法三个角度论证了它们之间都存在着本质区别,明确的指出:黎曼流形与外尔流形是二种不同的流形定义、不同的数学思想、不同的数学方法。 b). 本文讨论了两种流形之间关系,指出外尔流形是从光滑曲面角度发展了黎曼流形。
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The Essential Differences between Riemann manifold and Weyl manifold
Abstract:Riemannian manifold and Weyl manifold are two different manifold concepts. But, in many literature, not Weyl manifold and Riemannian manifold explicit discrimination.Or is the definition of the content of Weyl manifold is a Riemannian manifold as the definition of the content, or is the Weyl manifold with the Riemannian manifold confused, or is definition of the Weyl manifold is a Riemannian manifold as a clear mathematical description, etc. In view of each wrong viewpoint,We made the following innovation work: a). Pointing out: two kinds manifolds all have difference on manifolds definition, mathematics thought and mathematics method; b). Weyl manifold has developed Riemannian manifold from smooth surface.
Keywords: Riemannian manifold Weyl manifold Differences
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