Vitali的广义绝对微分学

IF 0.7 2区哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE

Archive for History of Exact Sciences Pub Date : 2021-05-24 DOI:10.1007/s00407-021-00273-4

Alberto Cogliati

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引用次数: 1

摘要

本文分析了1923年至1932年期间朱塞佩·维塔利对微分几何的贡献。特别是，Vitali的雄心勃勃的项目，详细讨论了作为Ricci Curbastro张量微积分扩展的广义微分学。特别注意在埃内斯托·帕斯卡的形式理论的背景下描述维塔利微积分的起源，并对导致协变导数的全面概念的过程进行分析。最后，结合博托洛蒂和博姆皮亚尼的后续著作，讨论了维塔利理论的接受问题。

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Vitali’s generalized absolute differential calculus

The paper provides an analysis of Giuseppe Vitali’s contributions to differential geometry over the period 1923–1932. In particular, Vitali’s ambitious project of elaborating a generalized differential calculus regarded as an extension of Ricci-Curbastro tensor calculus is discussed in some detail. Special attention is paid to describing the origin of Vitali’s calculus within the context of Ernesto Pascal’s theory of forms and to providing an analysis of the process leading to a fully general notion of covariant derivative. Finally, the reception of Vitali’s theory is discussed in light of Enea Bortolotti and Enrico Bompiani’s subsequent works.

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来源期刊

Archive for History of Exact Sciences 管理科学-科学史与科学哲学

CiteScore

1.30

自引率

20.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Archive for History of Exact Sciences casts light upon the conceptual groundwork of the sciences by analyzing the historical course of rigorous quantitative thought and the precise theory of nature in the fields of mathematics, physics, technical chemistry, computer science, astronomy, and the biological sciences, embracing as well their connections to experiment. This journal nourishes historical research meeting the standards of the mathematical sciences. Its aim is to give rapid and full publication to writings of exceptional depth, scope, and permanence.