2025/02/04 by Branding, V., Montaldo, S., Nistor, S. +2
#Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2502.02510
The conformal bienergy functional E2c was recently introduced as a modified version of the classical bienergy functional E2 in order to ensure the validity of some conformal invariance properties. The critical points of E2c are called conformal-biharmonic and denoted c-biharmonic. In this paper we study the c-biharmonic hypersurfaces Mm with constant principal curvatures in the product space \mathbb Lm(ε) × ℝ , where \mathbb Lm(ε) denotes a space form of constant sectional curvature ε . Specifically, we demonstrate that Mm is either totally geodesic or a cylindrical hypersurface of the form Mm-1 × ℝ , where Mm-1 is a c-biharmonic isoparametric hypersurface in \mathbb Lm(ε) . To provide further insight, we describe the structure of c-biharmonic isoparametric hypersurfaces in space forms. In the final part, as a preliminary effort to understand c-biharmonic hypersurfaces Mm in \mathbb Lm(ε) × ℝ with non constant mean curvature, we establish that a totally umbilical c-biharmonic hypersurface must necessarily be totally geodesic.