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 ...

Crystals may seem flawless, but deep inside they contain tiny structural imperfections that dramatically influence their strength and behavior. Researchers from The University of Osaka have used the ...

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 ...