The theorem of Fáry and Milnor for Hadamard manifolds
The author shows that the total curvature of a knotted curve lying in a 3-dimensional Hadamard manifold is greater or equal to \(4\phi \). In the proof, he adapts to Hadamard manifolds the work by \textit{E. Pannwitz} [Math. Ann. 108, 629-672 (1933; Zbl 0007.23104)] for a knotted curve in Euclidean space \(E^n\).
scientific article; zbMATH DE number 1180667