Existence of Metrics with Prescribed Scalar Curvature on the Volume Element Preserving Deformation

摘要

In this paper,we obtain two results on closed Reimainnian manifold $M\times[0,T]$.When $T$ is small enough,to any prescribed scalar curvature, theexistence and uniqueness of metrics are obtained on the volume elementpreserving deformation.When $T$ is large and the given scalar curvature issmall enough,the same result holds.