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Journal Articles Proceedings in Applied Mathematics and Mechanics Year : 2015

The role of virtual work in Levi-Civita's parallel transport

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Abstract

According to current history of science, Levi-Civita introduced parallel transport solely to give a geometrical interpretation to the covariant derivative of absolute differential calculus. Levi-Civita, however, searched a simple computation of the curvature of a Riemannian manifold, basing on notions of the Italian school of mathematical physics of his time: holonomic constraints, virtual displacements and work, which so have a remarkable, if not dominant, role in the origin of parallel transport.
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Origin : Files produced by the author(s)
Origin : Files produced by the author(s)

Dates and versions

hal-01244535 , version 1 (26-12-2015)

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Giuseppe Iurato, Giuseppe Ruta. The role of virtual work in Levi-Civita's parallel transport. Proceedings in Applied Mathematics and Mechanics, 2015, 15 (1), pp.705-1706. ⟨10.1002/pamm.201510342⟩. ⟨hal-01244535⟩
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