On the curvature of the diffeomorphism group
Let \(\text{SDIFF}(M)\) denote the group of diffeomorphisms preserving Riemannian density on a closed manifold \(M\). Using the results of \textit{V. I. Arnol'd} [Ann. Inst. Fourier 16, 319--361 (1966; Zbl 0148.45301)] the author obtains an expression for the sectional curvature of \(\text{SDIFF}(M)\) and establishes its negativeness for locally Euclidean \(M\).
scientific article; zbMATH DE number 727085