𝑂(2)×𝑂(2)-invariant hypersurfaces with constant negative scalar curvature in 𝐸⁴

Abstract

We use the method of equivariant differential geometry to prove the existence of a complete hypersurface with constant negative scalar curvature in E n ( n ≥ 4 ) {E^n}(n \geq 4) . This is the first example of a complete hypersurface with constant negative scalar curvature in E n ( n ≥ 4 ) {E^n}(n \geq 4) .