= Solution
The <Cheeger-Gromoll splitting theorem> states that a complete connected <Riemannian manifold> with nonnegative <Ricci curvature> that contains a <line in a Riemannian manifold> is isometric to a <Riemannian product>
$$
N\times\mathbb R.
$$
The <Hadamard-Cartan theorem> states that if a complete simply connected Riemannian manifold has nonpositive <sectional curvature>, then for every point $p$ its <exponential map>
$$
\exp_p:T_pM\longrightarrow M
$$
is a diffeomorphism. In particular, the manifold is diffeomorphic to Euclidean space and is <contractible space>[contractible].
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