In 4D, we cannot use triangles directly (we could use their higher-dimensional counterparts if we want to classify 3-manifolds), so more complex formulations of

In 4D, we cannot use triangles directly (we could use their higher-dimensional counterparts if we want to classify 3-manifolds), so more complex formulations of curvature are required. I am no expert in curvature myself, but I would wager that researchers would use Ricci curvature here. There's also a nice connection to the Poincare conjecture. I was planning on tackling that in another article. See MathOverflow for an interesting discussion on this subject: https://mathoverflow.net/a/9717 https://mathoverflow.net/a/9717