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Hadamard manifold

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In mathematics, a Hadamard manifold, named after Jacques Hadamard — sometimes called a Cartan–Hadamard manifold, after Élie Cartan — is a Riemannian manifold (M, g) that is complete and simply-connected, and has everywhere non-positive sectional curvature.

Examples

  • The real line R with its usual metric is a Hadamard manifold with constant sectional curvature equal to 0.
  • Standard n-dimensional hyperbolic space Hn is a Hadamard manifold with constant sectional curvature equal to −1.

    • References

    Hadamard manifold Wikipedia
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