Abstract
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 Riemannian products $$ {S}^{n-1}(a)\times {S}^1\left(\sqrt{1-{a}^2}\right),\kern0.5em {a}^2=1/\left(1+{K}^{{\scriptscriptstyle \frac{2}{n-2}}}\right)\mathrm{or}\kern0.5em {S}^{n-1}(a)\times {H}^1\left(-\sqrt{1+{a}^2}\right),\kern0.5em {a}^2=1/\left({K}^{{\scriptscriptstyle \frac{2}{n-2}}}-1\right). $$
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.