Hadamard manifold

Examples

The Euclidean space ${\displaystyle {\mathbb{R}}^n}$ with its usual metric is a Cartan–Hadamard manifold with constant sectional curvature equal to ${\displaystyle 0.}$

Standard ${\displaystyle n}$-dimensional hyperbolic space ${\displaystyle {\mathbb{H}}^n}$ is a Cartan–Hadamard manifold with constant sectional curvature equal to ${\displaystyle -1.}$