Kirchhoff elastic rods in five-dimensional space forms whose centerlines are not helices

Kawakubo, Satoshi

doi:10.1016/j.geomphys.2013.10.020

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Cited by 4 publications

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“…RM frames in Riemannian manifolds are used in the study of the structure equations for the evolution of a curve embedded in an n-dimensional Riemannian manifold with constant curvature (see, e.g., [14,23]) or a symmetric Riemannian space (see [3]). They are also used in the study of mathematical models of equilibrium configurations of thin elastic rods (see, e.g., [12] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

Geometric properties of rotation minimizing vector fields along curves in Riemannian manifolds

Etayo¹

2018

Turk J Math

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Rotation minimizing (RM) vector fields and frames were introduced by Bishop as an alternative to the Frenet frame. They are used in CAGD because they can be defined even when the curvature vanishes. Nevertheless, many other geometric properties have not been studied. In the present paper, RM vector fields along a curve immersed into a Riemannian manifold are studied when the ambient manifold is the Euclidean 3-space, the hyperbolic 3-space, and a Kähler manifold.

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Section: Introductionmentioning

confidence: 99%