This paper contains the introduction of the conformal curvature tensor now known as the Weyl tensor, which is widely used in geometry and gravity theory. Its classification by Petrov type has played a major role in, for example, studies of exact solutions and of gravitational radiation. The paper also introduces what is now called Weyl geometry, a generalization of Riemannian geometry which has been used in gravity theories alternative to general relativity, and contains ideas leading on to Weyl’s concept of projective curvature.

中文翻译：

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再版：Hermann Weyl 的纯无穷小几何

本文介绍了现称为外尔张量的共形曲率张量，该张量在几何和引力理论中得到广泛应用。它按彼得罗夫类型分类在例如精确解和引力辐射的研究中发挥了重要作用。该论文还介绍了现在称为外尔几何的东西，它是黎曼几何的一种推广，已用于替代广义相对论的引力理论，并包含导致外尔射影曲率概念的思想。