Hadamard manifold

Hadamard manifold

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 H"n" is a Hadamard manifold with constant sectional curvature equal to −1.

ee also

* Cartan–Hadamard theorem
* Hadamard space

References

*cite journal|last = Mourougane|first = Christophe|title = Interpolation in non-positively curved Kähler manifolds|journal = Arxiv.org|date = 7 Mar 2001|url = http://arxiv.org/pdf/math/0103045


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