Deforming metrics in the direction of their Ricci tensors

  title={Deforming metrics in the direction of their Ricci tensors},
  author={Dennis DeTurck},
  journal={Journal of Differential Geometry},
  • D. DeTurck
  • Published 1983
  • Mathematics
  • Journal of Differential Geometry
In [4], R. Hamilton has proved that if a compact manifold M of dimension three admits a C Riemannian metric g0 with positive Ricci curvature, then it also admits a metric g with constant positive sectional curvature, and is thus a quotient of the sphere S. In fact, he shows that the original metric can be deformed into the constant-curvature metric by requiring that, for t ≥ 0, x ∈ M and g = g(t, x), 
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Deforming metrics in the direction of their Ricci tensors
  • J. Differential Geom
  • 1983