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.
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
When are curves tangent to hypersurfaces?
Given a curve and a hypersurface, both in Euclidean space, how can we tell if the curve is tangent to the hypersurface?
Torsion, curvature, and parallel transport
An expository note on the notions of curvature and torsion of a general linear connection on the tangent bundle.
A Characterization of Geodesics
About the Einstein-Infeld-Hoffmann theorem characterizing geodesics.
Simulating Closed Cosmic Strings
One of my current research interests is in the geometry of constant-mean-curvature time-like submanifolds of Minkowski space. A special …
Bundles and derivatives
Expository article on the geometric notion of derivatives.
Conformal compactification of type (p,q) pseudo-Euclidean spaces
We explain how to conformally compactify pseudo-Euclidean spaces with $(p,q)$ signature.
The non-existence of black holes in (2+1) dimensional general relativity
We show that trapped surfaces cannot exist in (2+1) dimensional relativity.