References
- J. Arroyo and O. J. Garay, Closed free hyperelastic curves in the hyperbolic plane and Chen-Willmore rotational hypersurface, Israel Journal of Mathematics 138 (2013), 171-187. https://doi.org/10.1007/BF02783425
- J. Arroyo, O. J. Garay and J. J. Mencia, Closed free hyperelastic curves in real space forms, Proceeding of the XII Fall Workshop on Geometry and Physics, Coimbra (2013), 1-13.
- R. Gilmore, Lie Groups, Physics and Geometry, Cambridge University Press., New York, 2008.
- J. Langer and D. A. Singer, The total squared curvature of closed curves, Journal of Differential Geometry 20(1) (1984), 1-22. https://doi.org/10.4310/jdg/1214438990
- L. Noakes, G. Heinzinger and B. Paden, Cubic splines on curved spaces, IMA Journal of Mathematical Control and Information 6(4) (1989), 465-473. https://doi.org/10.1093/imamci/6.4.465
- L. Noakes, Null cubics and Lie quadratures, Journal of Mathematical Physics 44(3) (2003), 1436-1448. https://doi.org/10.1063/1.1537461
- B. O'Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press., New York, 1993.
- T. Popiel and L. Noakes, Elastica in SO (3), J. Aust. Math. Soc 83(1) (2007), 105-124. https://doi.org/10.1017/S1446788700036417
- T. Popiel, Geometrically-defined curves in Riemannian manifolds, Ph.D. Thesis, The University of Western Australia, School of Mathematics and Statistics 2007.
- D. A. Singer, Lectures on elastic curves and rods, Amer. Inst. Phys., Melville, NY, 1002 (2008).