Non-Euclidean elasticity for rods and almost isometric embeddings of geodesic tubes

Milan Kroemer, Stefan Müller

We consider a geodesic $\gamma$ of length $2L$ in an oriented Riemannian manifold $(\mathcal{M},g)$ and a thin tube ${\Omega }_h^{\ast }$ around $\gamma$ of radius $h$. We study an 'elastic' energy per un…