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 ...

Differential geometry of curves and surfaces examines how smooth lines and two-dimensional manifolds bend and twist within ambient spaces. Beginning with the pioneering work on Frenet–Serret formulae ...

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 ...

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, ...