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

Zhi-Zhang Wang

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

Differential Geometry 2007-05-23 v1 Metric Geometry

Authors: Zhi-Zhang Wang

Abstract

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.

Keywords

scalar curvature volume element preserving deformation Riemannian manifold existence and uniqueness closed manifold

Cite

@article{arxiv.math/0612686,
  title  = {Existence of Metrics with Prescribed Scalar Curvature on the Volume Element Preserving Deformation},
  author = {Zhi-Zhang Wang},
  journal= {arXiv preprint arXiv:math/0612686},
  year   = {2007}
}

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32 pages

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