Hypersurfaces with nonzero constant Gauss – Kronecker curvature in $M^{n+1}(±1)$

• Date: 2016
• Main Authors: Shu, Shichang, Zhu, Tianmin, Шу, Шичанґ, Чжу, Тяньмін
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2016
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/1940
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We study hypersurfaces in a unit sphere and in a hyperbolic space with nonzero constant Gauss – Kronecker curvature and two distinct principal curvatures one of which is simple. Denoting by $K$ the nonzero constant Gauss – Kronecker curvature of hypersurfaces, we obtain some characterizations of the...