2013 Volume 34 Issue 1 Pages 9-14
Geometric curvature of a low-dimensional host material often leads to drastic changes in physical properties of the system living upon it. In this article, I give a bird's-eye review on the theoretical progresses on the geometry-property relations, i.e., intriguing correlation between geometric curvature and physical property of the material considered. Some differential-geometry-based approaches that are aimed at quantitative description of physical systems confined to curved surfaces are presented.