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