In this paper, we give examples of Kirchhoff rod centerlines fully immersed in higher-dimensional space forms. More precisely, we prove that any helix in a space form is a Kirchhoff rod centerline. These examples imply the difference of the geometric properties between Kirchhoff rod centerlines and elasticae.
"Kirchhoff elastic rods in higher-dimensional space forms." Proc. Japan Acad. Ser. A Math. Sci. 87 (1) 5 - 9, January 2011. https://doi.org/10.3792/pjaa.87.5