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Riemannian Geometry is a subfield of Differential Geometry, which specifically studies "Riemannian Manifolds", manifolds with "Riemannian Metrics", which means that they are equipped with continuous inner products.

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Connectedness of the space of negatively curved metrics of a compact 3-manifold

Is the space of metrics of negative sectional curvature over a closed 3-manifold connected? If so, in what paper is this result stated? Note: as the Ricci flow hyperbolizes negatively curved metrics, …
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