Work

Polyharmonic curves in semi-Riemannian manifolds

Year: 2025

Type: article

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.

Source: Journal of Mathematical Analysis and Applications

DOI: 10.1016/j.jmaa.2025.130152

Authors: S. Montaldo, A. Ratto, A. Sanna

Institution: University of Cagliari

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Fondazione di Sardegna, European Commission