2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152593We calculate the Riemann curvature tensor and sectional curvature for the Lie group of volume-preserving diffeomorphisms of the Klein bottle and projective plane. In particular, we investigate the sign of the sectional curvature, and find a possible disagreement with a theorem of Lukatskii. We suggest an amendment to this theorem.18 pages, LATEXHigh Energy Physics - TheoryFunctional AnalysisDifferential Geometrytext