# 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.

### Lengths of Parallel Curves

Let's start with something simple: Given a circle with radius $R$, draw a concentric circle with radius 1 larger. How much longer is …

### Matter field from diffeomorphism: on a theme of Capoferri and Vassiliev

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

### Lie Groups

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

### Dynamics of a Rigid Body

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 …

### Models of Hyperbolic Plane

Some notes on the relationship between different models of hyperbolic plane

### The Translation Action on Function Spaces

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

### Newton-Cartan Gravity

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

### Parallel Volume Forms and Affine Differential Geometry

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

### The Nirenberg Trick and Wave Maps

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

### Poohsticks and differential geometry

Random thought: Poohsticks illustrates well Lie differentiation