This is an arXiv category tag: it contains differential geometry and Riemannian geometry. Roughly speaking the notion of geometry here refers to how one can measure things on manifolds.

I try to reformulate an idea of Capoferri and Vassiliev in the infinitesimal limit and see where it goes.

Some introductory notes about the definition and geometry of Lie groups, and their analysis.

This post is about the formulation of the dynamics of a rigid body, under rotations, as dynamics on a Lie group. I'm writing this to …

Some notes on the relationship between different models of hyperbolic plane

Preliminaries Here's something I learned from Chongchun Zeng of Georgia Tech, while chatting over some hors-d'oeuvres at the AMS …

A quick introduction of Newton-Cartan theory, which is a sort of Newtonian limit of general relativity from a geometric point of view.

A brief introduction to affine differential geometry and the notion of preferred volume forms.

The "Nirenberg trick" or "Nirenberg transformation" is the observation1 that the semilinear wave equation …

Random thought: Poohsticks illustrates well Lie differentiation

Given a curve and a hypersurface, both in Euclidean space, how can we tell if the curve is tangent to the hypersurface?