6533b822fe1ef96bd127d559
RESEARCH PRODUCT
The role of virtual work in Levi-Civita's parallel transport
Giuseppe IuratoGiuseppe Rutasubject
AlgebraRicci calculusCurrent (mathematics)IntersectionParallel transportComputer scienceCalculusVirtual workRiemannian manifoldCurvatureCovariant derivativedescription
The current literature on history of science reports that Levi-Civita’s parallel transport was motivated by his attempt to provide the covariant derivative of the absolute differential calculus with a geometrical interpretation (For instance, see Scholz in The intersection of history and mathematics, Birkhauser, Basel, pp 203–230, 1994, Sect. 4). Levi-Civita’s memoir on the subject was explicitly aimed at simplifying the geometrical computation of the curvature of a Riemannian manifold. In the present paper, we wish to point out the possible role implicitly played by the principle of virtual work in Levi-Civita’s conceptual reasoning to formulate parallel transport.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2015-10-01 | PAMM |