A note on the \(p\)-elastica in a constant sectional curvature manifold (Q557212)

Following \textit{J.\ Langer} and \textit{D.\ A.\ Singer} [J.\ Differ.\ Geom.\ 20, 1--22 (1984; Zbl 0554.53013)], this paper studies critical points ``\(\gamma\)'' of functionals of the type \(\int_\gamma p(k)\,ds\), where \(\gamma(s)\) is an arc length parametrization of a curve with geodesic curvature \(k\) in a constant curvature Riemannian manifold, and \(p\) is a polynomial of degree \(\geq 2\). The corresponding Euler-Lagrange equations allow to express \(k\) by quadratures. In the case of Euclidean 3-space, more details can be derived.