Positive curvature, like that on a sphere, implies a finite universe, while zero curvature, as on a flat plane or negative ...

General Relativity reinterprets the force of gravity not as a traditional force but as a manifestation of the curvature of spacetime. Its formulation rests on a rigorous mathematical framework built ...

On a compact n-dimensional manifold, it is well known that a critical metric of the total scalar curvature, restricted to the space of metrics with unit volume is Einstein. It has been conjectured ...

Describing natural phenomena with geometric language is one of the most important achievements of modern physics. In the context of general relativity, Einstein treats spacetime as a dynamic geometric ...

Riemannian manifolds or geodesic metric spaces of finite or infinite dimension occur in many areas of mathematics. We are interested in the interplay between their local geometry and global ...