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- 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: SU(1,1)
Riemannian metric on SL(2,R)- explicit formula
Riemannian metric is usually expressed through its metric tensor. For instance in Conformally Euclidean geometry of the upper half-plane we were discussing the SL(2,R) invariant Riemannian metric on the upper half-plane and came out with the formula: (1) Riemannian … Continue reading
Posted in Hyperbolic geometry, SU(1,1)
5 Comments
Parametrization of SL(2,R)
We are going to discuss Riemannian metric on SL(2,R), which will be more difficult than Riemannian metric on the Poincare disk or on the upper half-plane , because SL(2,R) is three-dimensional. In fact it will be a pseudo-Riemannian metric, because … Continue reading
Posted in Hyperbolic geometry, SU(1,1)
1 Comment
Dedekind tessellation or circles all the way down
“Turtles all the way down” is an expression of the infinite regress problem in cosmology posed by the “unmoved mover” paradox. The metaphor in the anecdote represents a popular notion of the model that Earth is actually flat and is … Continue reading
Posted in Hyperbolic geometry, Mathematica, SU(1,1)
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