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/

Zendy Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

In this paper, we introduce a one-parameter family of Legendre curves in the unit spherical bundle over the unit sphere and the curvature. We give the existence and uniqueness theorems for one-parameter families of spherical Legendre curves by using the curvatures. Then we define an envelope for the one-parameter family of Legendre curves in the unit spherical bundle. We also consider the parallel curves and evolutes of one-parameter families of Legendre curves in the unit spherical bundle and their envelopes. Moreover, we give relationships among one-parameter families of Legendre curves in the unit spherical bundle over the unit sphere and one-parameter families of Legendre curves in the unit tangent bundle over the Euclidean plane.

Envelopes of legendre curves in the unit spherical bundle over the unit sphere