A historical perspective on parallel transport: isometric immersions and Foucault precession

Franco Cardin; Rossana Tazzioli

doi:10.5802/crmath.809

Article de recherche - Histoire des mathématiques

A historical perspective on parallel transport: isometric immersions and Foucault precession
[Une perspective historique sur le transport parallèle : immersions isométriques et précession de Foucault]

Franco Cardin ¹ ; Rossana Tazzioli ²

¹Dipartimento di Matematica Tullio Levi-Civita, Università di Padova, Italy
²Laboratoire Paul Painlevé, Université de Lille, France

Comptes Rendus. Mathématique, Volume 364 (2026), pp. 13-26

Abstract (VO)
Résumé

This paper contributes to the historical understanding of the developments surrounding the Levi-Civita parallel transport problem, exploring its connections with the local problem of isometric immersions and alternative proposals. Additionally, it highlights one of its remarkable applications: the geometric interpretation of Foucault’s pendulum precession. It also recalls how other geometric explanations of this phenomenon emerged in the context of Berry and Hannay phases.

Cet article contribue à la compréhension historique des développements liés au problème du transport parallèle de Levi-Civita, en explorant ses liens avec le problème local des immersions isométriques ainsi qu’avec des propositions alternatives. Il met également en lumière l’une de ses applications remarquables : l’interprétation géométrique de la précession du pendule de Foucault. Enfin, il rappelle comment d’autres explications géométriques de ce phénomène ont émergé dans le contexte des phases de Berry et de Hannay.

Reçu le : 2025-09-06
Révisé le : 2025-11-20
Accepté le : 2025-11-20
Publié le : 2026-02-16

DOI : 10.5802/crmath.809

Classification : 53Z05, 53A17, 53-03
Keywords: Parallel transport, isometric immersions, Foucault pendulum precession
Mots-clés : Transport parallèle, immersions isométriques, précession du pendule de Foucault

Affiliations des auteurs :

Franco Cardin ¹ ; Rossana Tazzioli ²

¹ Dipartimento di Matematica Tullio Levi-Civita, Università di Padova, Italy
² Laboratoire Paul Painlevé, Université de Lille, France

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     journal = {Comptes Rendus. Math\'ematique},
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Franco Cardin; Rossana Tazzioli. A historical perspective on parallel transport: isometric immersions and Foucault precession. Comptes Rendus. Mathématique, Volume 364 (2026), pp. 13-26. doi: 10.5802/crmath.809

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