Mathematicians already knew that the way in which curvature varies from place to place inside a ‘Riemannian manifold’ — the mathematical jargon for curved space — determines the shortest ...

Many interesting classes of Riemannian manifolds are precompact in the Gromov ... In particular, we will study manifolds, their diffeomorphisms and embeddings, and positive scalar curvature metrics on ...

Other goals include structure results for singular Riemannian foliations in nonnegative curvature and a differentiable diameter pinching theorem. Hamilton's Ricci flow is a (weakly parabolic) ...

Due to the curvature, however ... In terms of mathematics, general relativity is based on pseudo-Riemannian geometry, which is a mathematical language capable of describing most of the typical ...

2. Don Colladay, Jeffrey Langford, and Patrick McDonald, Comparison Results, Exit Time Moments, and Eigenvalues on Riemannian Manifolds with a Lower Ricci Curvature Bound, The Journal of Geometric ...

Paris, Ser I. 339 (2004), 621-624 (with J. Yue) Covariants, joint invariants and the equivalence problem in the invariant theory of Killing tensors defined in pseudo-Riemannian manifolds of constant ...