Flat tori in three-dimensional space and convex integration
Flat tori in three-dimensional space and convex integration
It is well-known that the curvature tensor is an isometric invariant of C 2 Riemannian manifolds. This invariant is at the origin of the rigidity observed in Riemannian geometry. In the mid 1950s, Nash amazed the world mathematical community by showing that this rigidity breaks down in regularity C 1 …