Complete -hypersurfaces with constant squared norm of the second fundamental form in the Euclidean space \mathbb R^{4}
Volume 175 / 2024
Colloquium Mathematicum 175 (2024), 187-210
MSC: Primary 53E10; Secondary 53C40
DOI: 10.4064/cm9060-2-2024
Published online: 17 May 2024
Abstract
Under the assumption that the quasi-Gauss–Kronecker curvature K_{q} is identically zero, we give a complete classification of 3-dimensional complete \lambda -hypersurfaces with constant squared norm S of the second fundamental form in the Euclidean space \mathbb R^{4}, where S=\sum_{i,j}h^{2}_{ij}, K_{q}= \mathrm{det}(h_{ij}-\frac{1}{3}H\delta _{ij}), with h_{ij} being the components of the second fundamental form.
