Differential geometry studies smooth shapes and spaces known as manifolds, using tools such as tangent spaces, curvature and connections to describe their local and global properties.

Differential geometry studies smooth manifolds—spaces that locally resemble Euclidean domains but may exhibit intricate global topology—and explores how curvature measures encode geometric and ...

In the field of Differential Geometry we are concerned with Riemannian manifolds or more generally (inner) metric spaces. We are interested in the interplay between their curvature and global ...