Langer, Joel; Singer, David A. The total squared curvature of closed curves. (English) Zbl 0554.53013 J. Differ. Geom. 20, 1-22 (1984). The authors study the total squared curvature \(\oint k^ 2 ds\) of closed curves in spaces of constant curvature. The critical points of this functional are called closed free elastica. In the case of curves in a zero-dimensional space form a complete classification of such elastica is given. For arbitrary closed curves in the hyperbolic plane the authors obtain the following inequality: \(\oint k^ 2 ds\geq 4\pi\). Reviewer: U.Pinkall Cited in 8 ReviewsCited in 155 Documents MSC: 53A35 Non-Euclidean differential geometry 53A04 Curves in Euclidean and related spaces 58E99 Variational problems in infinite-dimensional spaces Keywords:total squared curvature; free elastica; space form; hyperbolic plane Citations:Zbl 0554.53014 PDFBibTeX XMLCite \textit{J. Langer} and \textit{D. A. Singer}, J. Differ. Geom. 20, 1--22 (1984; Zbl 0554.53013) Full Text: DOI