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 ...

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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 ...

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 ...

Conformal geometry is the study of structures on manifolds that remain invariant under angle-preserving transformations. At its core is the notion of a conformal class, a collection of metrics that ...

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, ...