Category
page 1Theorems in Riemannian geometry
Hopf–Rinow theorem
theorem that, for a Riemannian manifold, geodesic completeness is equivalent to completeness as a metric space
Nash embedding theorem
theorem
Myers's theorem
theorem applying to Riemannian manifolds
fundamental theorem of Riemannian geometry
unique existence of the Levi-Civita connection
Cartan–Hadamard theorem
On the structure of complete Riemannian manifolds of non-positive sectional curvature
soul theorem
mathematical theorem
Gromov's compactness theorem
On when a set of compact Riemannian manifolds of a given dimension is relatively compact
Synge's theorem
Relates the curvature of a Riemannian manifold to its topology
sphere theorem
theorem stating that a complete, simply-connected, n-dimensional Riemannian manifold with sectional curvature taking values in the interval (1, 4] is homeomorphic to the n-sphere