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.

Application of tools from differential geometry and Lie groups to problems in dynamics, controllability, and motion planning for mechanical systems, particularly with non-Euclidean configuration ...

The study of mean curvature occupies a central place in modern differential geometry, linking geometric analysis, partial differential equations and applications across physics and materials science.