Cartan-Hadamard Theorem

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Theorem

Let $M$ be a complete connected $n$-dimensional Riemannian manifold.

Suppose all sectional curvatures of $M$ are less than or equal to zero.


Then the universal covering space of $M$ is diffeomorphic to $\R^n$.


Proof



Source of Name

This entry was named for √Člie Joseph Cartan and Jacques Salomon Hadamard.


Sources