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Recent Posts
- Kronecker generalized deltas and Levi-Civita epsilons 2026/01/09
- It’s all about permutations 2025/12/28
- Densities 2025/12/21
- Tensors on a picnic 2025/12/14
- Tensors are geometric objects 2025/12/10
- Conformal structure – until the puppy grows up 2025/12/07
- Growing Out of the Sandbox 2025/12/02
- Blog reincarnation with analytic idealism 2025/11/30
- Minkowski patches in the Einstein universe 2025/11/27
- Floating in the Einstein Universe 2025/11/24
- Comments on Clifford algebras 2019/01/24
- Comment on “Could ordinary quantum mechanics be just fine for all practical purposes?” by Alexey Nikulov 2018/03/08
- Spinning Top – Space Odity 2017/05/28
- Geodesics of left invariant metrics on matrix Lie groups – Part 2 Conservation laws 2017/05/26
- Geodesics of left invariant metrics on matrix Lie groups – Part 1 2017/05/24
- Killing vectors, geodesics, and Noether’s theorem 2017/05/23
- SL2R as anti de Sitter space cont. 2017/05/15
- Becoming anti de Sitter 2017/05/14
- SL(2,R) Killing vector fields in coordinates 2017/05/11
- Riemannian metrics – left, right and bi-invariant 2017/05/09
- Riemannian metric on SL(2,R)- explicit formula 2017/05/08
- Riemannian metric on SL(2,R) 2017/05/07
- Parametrization of SL(2,R) 2017/05/06
- Curvature of the upper half-plane 2017/05/05
- Geodesics on upper half-plane factory direct 2017/05/04
- Einstein the Stubborn 2017/05/03
- Dedekind tessellation on the Poincaré disk 2017/05/02
- Dedekind tessellation or circles all the way down 2017/04/30
- Real magic – space-time in Lie algebra 2017/04/29
- Geodesics on the upper half-plane – parametrization 2017/04/28
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Category Archives: Geometry
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 Einstein Universe, null cones, photons, projectivization
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
Geodesics of left invariant metrics on matrix Lie groups – Part 1
An elegant derivation of geodesic equations for left invariant metrics has been given by B. Kolev in his paper “Lie groups and mechanics. An introduction”. Here we will derive these equations using simple tools of matrix algebra and differential geometry, … Continue reading
Posted in Geometry
7 Comments
