2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152609We obtain an expression for the curvature of the Lie group SDiff$\cal M$ and use it to derive Lukatskii's formula for the case where $\cal M$ is locally Euclidean. We discuss qualitatively some previous findings for SDiff$S^{2}$ in conjunction with our result.10 pagesHigh Energy Physics - TheoryDifferential Geometrytext