Differential manifolds provide higher dimensional generalizations of surfaces. They appear in a very natural manner in many areas of mathematics and physics. On a differential manifold or more ...

Algebraic geometry and differential geometry form two pillars of modern geometry, each providing its own language and techniques to study shapes and spaces. Algebraic geometry examines solution sets ...

Differential geometry has long found applications in physics in general relativity and related areas. More recently, it was proposed by Nielsen that the tools of differential geometry, when applied to ...

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 ...

I work in differential geometry and the application of geometry to the study of partial differential equations. Specifically, my work has focused on conservation laws, Backlund transformations, ...