2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/120570In this paper,we obtain two results on closed Reimainnian manifold $M\times [0,T]$.When $T$ is small enough,to any prescribed scalar curvature, the existence and uniqueness of metrics are obtained on the volume element preserving deformation.When $T$ is large and the given scalar curvature is small enough,the same result holds.32 pagesDifferential GeometryMetric Geometry53C21; 58J45; 35L70text