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

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

2006-12-22

arxiv.org/abs/math/0612686v1

Mathematics

Differential Geometry

32 pages

Scientific paper

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, 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.

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