Biharmonic Curves in Warped Product Manifolds $I{\times }_f{M}^n\left(c\right)$

Abstract

We explore the geometric properties of biharmonic curves in warped product manifolds of the form $I{\times }_f{M}^n(c)$, where $I$ is an open interval and $M^n(c)$ is a space of constant curvature. By establishing a main theorem, we analyze four distinct cases to reveal deeper curvature-related characteristics of these curves, including situations where they are slant. Finally, we construct two examples in $I{\times }_f{S}^2(1)$.

13 pages