# Deforming metrics in the direction of their Ricci tensors

@article{DeTurck1983DeformingMI, title={Deforming metrics in the direction of their Ricci tensors}, author={Dennis DeTurck}, journal={Journal of Differential Geometry}, year={1983}, volume={18}, pages={157-162} }

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),

## 388 Citations

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- Mathematics
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Deforming metrics in the direction of their Ricci tensors

- J. Differential Geom
- 1983