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math.DG2022★ 1 cited
On a notion of nonlocal curvature tensor
Roberto Paroni, Paolo Podio-Guidugli, Brian Seguin
In the literature various notions of nonlocal curvature can be found. Here we propose a notion of nonlocal curvature tensor. This we do by generalizing an appropriate representatio…
math.DG2017
On the Nonlocal Curvatures of Surfaces with or without Boundary
Roberto Paroni, Paolo Podio-Guidugli, Brian Seguin
For surfaces without boundary, nonlocal notions of directional and mean curvatures have been recently given. Here, we develop alternative notions, special cases of which apply to s…