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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider hypersurfaces in the real Euclidean space $\mathbb{R}^{n+1}$($n\geq2$) which are relatively normalized. We give necessary and sufficientconditions a) for a surface of negative Gaussian curvature in $\mathbb{R}^3$ tobe ruled, b) for a hypersurface of positive Gaussian curvature in$\mathbb{R}^{n+1}$ to be a hyperquadric and c) for a relative normalization tobe constantly proportional to the equiaffine normalization.

Characterizations of Ruled Surfaces in $\mathbb{R}^3$ and of Hyperquadrics in $\mathbb{R}^{n+1}$ via Relative Geometric Invariants