English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The rototranslation group  ℛ T is the group comprising rotations and translations of the Euclidean plane which is a 3-dimensional Lie group. In this paper, we use the Riemannian approximation scheme to compute sub-Riemannian limits of the Gaussian curvature for a Euclidean  C 2 -smooth surface in the rototranslation group away from characteristic points and signed geodesic curvature for Euclidean  C 2 -smooth curves on surfaces. Based on these results, we obtain a Gauss–Bonnet theorem in the rototranslation group.

The Sub-Riemannian Limit of Curvatures for Curves and Surfaces and a Gauss–Bonnet Theorem in the Rototranslation Group