Stability of \(O(p+1) \times O(p+1)\)-invariant hypersurfaces with zero scalar curvature in Euclidean space
The author classifies \(O(p+1)\times O(p+1)-\)invariant hypersurfaces with zero scalar curvature in \({\mathbb R}^{2p+2},p>1\) according to their profile curves and shows that there are complete and embedded examples. Then, by studying the Morse indices of complete examples, the author shows that there exists a nonplanar globally stable, embedded complete hypersurface with zero scalar curvature in \({\mathbb R}^{2p+2}.\) This stable example provides a counterexample in odd dimensions \(\geq 9\) to a Bernstein-type conjecture for immersions with zero scalar curvature.
scientific article; zbMATH DE number 1802371