math.DG

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.

In a previous post we discussed a little problem in "almost" Finsler geometry. In this post we will dissect some properties …
Last updated on 9 min read Mathematical Diversions

This post is inspired by: In the diagram a 1 meter rod, initially horizontal, rotates 90-degrees about endpoint B & then translates …
Last updated on 11 min read Mathematical Diversions

Let's start with something simple: Given a circle with radius $R$, draw a concentric circle with radius 1 larger. How much longer is …
Last updated on 3 min read mathematical diversions

I try to reformulate an idea of Capoferri and Vassiliev in the infinitesimal limit and see where it goes.
Last updated on 5 min read research

Some introductory notes about the definition and geometry of Lie groups, and their analysis.
Last updated on 19 min read expository

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 …
Last updated on 9 min read expository

Some notes on the relationship between different models of hyperbolic plane
Last updated on 6 min read expository

Preliminaries Here's something I learned from Chongchun Zeng of Georgia Tech, while chatting over some hors-d'oeuvres at the AMS …
Last updated on 6 min read expository

A quick introduction of Newton-Cartan theory, which is a sort of Newtonian limit of general relativity from a geometric point of view.
Last updated on 32 min read expository

A brief introduction to affine differential geometry and the notion of preferred volume forms.
Last updated on 13 min read expository