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 $I\times _{f}S^{2}(1)$.