Three-manifolds with positive Ricci curvature

@article{Hamilton1982ThreemanifoldsWP,
  title={Three-manifolds with positive Ricci curvature},
  author={Richard S. Hamilton},
  journal={Journal of Differential Geometry},
  year={1982},
  volume={17},
  pages={255-306}
}
  • R. Hamilton
  • Published 1982
  • Mathematics
  • Journal of Differential Geometry
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References

SHOWING 1-5 OF 5 REFERENCES
Spaces of Constant Curvature
This sixth edition illustrates the high degree of interplay between group theory and geometry. The reader will benefit from the very concise treatments of riemannian and pseudo-riemannian manifolds
Comparison theorems in Riemannian geometry
Basic concepts and results Toponogov's theorem Homogeneous spaces Morse theory Closed geodesics and the cut locus The sphere theorem and its generalizations The differentiable sphere theorem Complete
Harmonic Maps of Manifolds with Boundary
Harmonic maps.- Function spaces.- Semi-elliptic and parabolic equations.- The heat equation for manifolds.- Growth estimates and convergence.