Polyharmonic curves in semi-Riemannian manifolds

Montaldo, S.

;Ratto, A.;Sanna, A.

2026-01-01

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Abstract

Let ( M_t^m , g ) be a semi-Riemannian manifold of dimension m with a non-degenerate metric of index t , m ≥ 2 , 1 ≤ t ≤ m − 1 . The main aim of this paper is to investigate the existence of Frenet curves in ( M_t^m , 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_t^m( 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.