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

A spacelike surface in four-dimensional Lorentz-Minkowski spacetime throughthe lightcone has a meaningful lightlike normal vector field $\eta$. Severalsufficient assumptions on such a surface with non-degenerate $\eta$-secondfundamental form are established to prove that it must be a totally umbilicalround sphere. With this aim, a new formula which relates the Gauss curvaturesof the induced metric and of the $\eta$-second fundamental form is developed.Then, totally umbilical round spheres are characterized as the only compactspacelike surfaces through the lightcone such that its $\eta$-secondfundamental form is non-degenerate and has constant Gauss curvature two.Another characterizations of totally umbilical round spheres in terms of theGauss-Kronecker curvature of $\eta$ and the area of the $\eta$-secondfundamental form are also given.

Compact spacelike surfaces in four-dimensional Lorentz-Minkowski spacetime with a non-degenerate lightlike normal direction