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 give a full classification of complete rotationally invariant surfaceswith constant Gauss curvature in Berger spheres: they are either Clifford tori,which are flat, or spheres of Gauss curvature $K \geq K_0$ for a positiveconstant $K_0$, which we determine explicitly and depends on the geometry ofthe ambient Berger sphere. For values of $K_0 \leq K \leq K_P$, for a specificconstant $K_P$, it was not known until now whether complete constant Gausscurvature $K$ surfaces existed in Berger spheres, so our classificationprovides the first examples. For $K > K_P$, we prove that the rotationallyinvariant spheres from our classification are the only topological spheres withconstant Gauss curvature in Berger spheres.

Rotationally invariant constant Gauss curvature surfaces in Berger spheres