A 150-year-old geometry rule has been overturned after mathematicians found two different torus surfaces with identical ...

Differential geometry is the study of smooth manifolds and the intrinsic properties of spaces that can be described locally by Euclidean geometry. Within this expansive field, singularities represent ...

The study of algebraic structures and differential geometry has evolved into a dynamic interdisciplinary field that synthesises abstract algebraic concepts with the smooth variability of geometric ...

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 ...

Mathematics is one of the oldest disciplines of study. For all its antiquity, however, it is a modern, rapidly growing field. Only 70 years ago, mathematics might have been said to consist of algebra, ...

The spectrum of the canonical operator in the noncommutative 2-torus Tθ depending on the parameter θ ∈ [0,1] © Douglas Hofstadter's butterfly. Licensed under ...

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 ...