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.

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

An expository note on the notions of curvature and torsion of a general linear connection on the tangent bundle.

About the Einstein-Infeld-Hoffmann theorem characterizing geodesics.

One of my current research interests is in the geometry of constant-mean-curvature time-like submanifolds of Minkowski space. A special …

Expository article on the geometric notion of derivatives.

We explain how to conformally compactify pseudo-Euclidean spaces with $(p,q)$ signature.

We show that trapped surfaces cannot exist in (2+1) dimensional relativity.

Life is boring in low dimensions.

The relationship between gravitational red shift and the surface gravity of black holes is explained.

A bit of trivia (can't think of any use of it now) Theorem   Let $(M,g)$ be a two-dimensional compact Riemannian manifold with …