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arXiv · 2505.02194

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

Şaban Güvenç·Cihan Özgür
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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 $I\times _{f}S^{2}(1)$.

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Şaban Güvenç, Cihan Özgür. 2025-05-04. Biharmonic Curves in Warped Product Manifolds $I\times_{f}M^{n}\left( c\right) $. https://doi.org/10.55730/1300-0098.3670

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