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arXiv · 2506.16954

Polyharmonic curves in semi-Riemannian manifolds

Stefano Montaldo·Andrea Ratto·Antonio Sanna
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Abstract

Let $(M^m_t,g)$ be a semi-Riemannian manifold of dimension $m$ with a non-degenerate metric of \textit{index} $t$, $m\geq 2$, $1 \leq t \leq m-1$. The main aim of this paper is to investigate the existence of Frenet curves in $(M^m_t,g)$ which are polyharmonic of order $r$, shortly, $r$-harmonic. We shall focus primarily on the cases that the ambient space is a semi-Riemannian space form $N^m_t(c)$ of sectional curvature $c$, a ruled Lorentzian surface or a suitable, possibly warped, product space. We shall obtain existence, non-existence and classification results.

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Stefano Montaldo, Andrea Ratto, Antonio Sanna. 2025-06-20. Polyharmonic curves in semi-Riemannian manifolds. https://arxiv.org/abs/2506.16954

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