A metric on the manifold of immersions and its Riemannian curvature
\textit{E. Binz} [ibid. 89, 275-288 (1980; Zbl 0428.58006)] considered two canonical Riemannian metrics on the space of embeddings of a closed (n-1) dimensional manifold into \({\mathbb{R}}^ n\), and computed the geodesic sprays. Here we consider the space of immersions Imm(M,N) where M is without boundary, and we compute the covariant derivative (in the form of its connector) and the Riemannian curvature of one of these metrics, the nontrivial one. The setting is close to that used by \textit{P. Michor} [Manifolds of differentiable mappings (1980; Zbl 0433.58001)] and we refer the reader to this paper for notation.
scientific article; zbMATH DE number 3872325