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arXiv 2210.13239gr-qcphysics.hist-ph
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一般流形上的广义流形概念与黎曼曲率的一致几何规定

Notion of Parallelism on a Generic Manifold and Consequent Geometrical Specification of the Riemannian Curvature

Tullio Levi-Civita

摘要:

关于经典微分几何,本文讨论了T.列维-奇维塔介绍了平行的概念,为黎曼流形的任意尺寸。它还提供了一个几何解释的黎曼曲率,并在同一时间显着减少了数学形式主义相比,科学文献的时间。

英文摘要:

With regard to classical differential geometry, this paper written in 1916 by T. Levi-Civita introduces the notion of parallelism for a Riemannian manifold of arbitrary dimensions. It also provides a geometrical explanation for the Riemannian curvature and at the same time significantly reduces the mathematical formalism compared with the scientific literature of the time.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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