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.^[1][2]

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.

See also

• Cartan–Hadamard theorem
• Hadamard space

References

1. Li, Peter (2012). Geometric Analysis. Cambridge University Press. p. 381. ISBN 9781107020641.
2. Lang, Serge (1989). Fundamentals of Differential Geometry, Volume 160. Springer. pp. 252–253. ISBN 9780387985930.