The attendant parallel displacement operations also had natural algebraic interpretations in terms of the connection.
2.
Example : Parallel displacement along a circle of a three-dimensional ball embedded in two dimensions.
3.
The work of Levi-Civita focused exclusively on regarding connections as a kind of differential operator whose parallel displacements were then the solutions of differential equations.
4.
The Levi-Civita notions of intrinsic derivative and parallel displacement of a vector along a curve make sense on an abstract Riemannian manifold, even though the original motivation relied on a specific embedding
5.
The 1970s through the 1990s saw the succession of secular Jewish tourists to Sharon Springs by Hasidim and ultra-Orthodox Jewish visitors, fed in part by a parallel displacement in the nearby Borsht Belt.
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