Sato, Jocelino Stability of \(O(p+1) \times O(p+1)\)-invariant hypersurfaces with zero scalar curvature in Euclidean space. (English) Zbl 1036.53039 Ann. Global Anal. Geom. 22, No. 2, 135-153 (2002). 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. Reviewer: Sung-Eun Koh (Seoul) Cited in 1 ReviewCited in 6 Documents MSC: 53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) 53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature Keywords:equivariant geometry; scalar curvature; stability; Bernstein’s conjecture PDFBibTeX XMLCite \textit{J. Sato}, Ann. Global Anal. Geom. 22, No. 2, 135--153 (2002; Zbl 1036.53039) Full Text: DOI