Category Archives: Geometry

Geometry, especially curvature and geodesics

Conformal structure – until the puppy grows up

On my other blog, I promised Anna—the ever‑curious Reader—that I would finally tackle the subject of conformal structure. So here it begins: a gentle introduction to a concept that admits many gateways. Precise definitions abound online, of course, and one … Continue reading

Posted in Conformal structure, Geometry | Tagged , | 26 Comments

Floating in the Einstein Universe

This post is the third chapter of the “Primer” saga, based on   “A primer on the (2 + 1) Einstein universe” – a paper is written by five mathematicians, T. Barbot, V. Charette, T. Drumm, M. Goldmann, K. Melnick, … Continue reading

Posted in Compactified Minkowski space, Geometry | Tagged , , , | 1 Comment

Geodesics of left invariant metrics on matrix Lie groups – Part 2 Conservation laws

In the last post, Geodesics of left invariant metrics on matrix Lie groups – Part 1,we have derived Arnold’s equation – that is a half of the problem of finding geodesics on a Lie group endowed with left-invariant metric. Suppose … Continue reading

Posted in Euler's equations, Geometry | 2 Comments