I am calculating the connection forms for the case of a Poincaré Disk but
the diagonal elements appear to be non-zero
`M = Manifold(2, 'M', r'\mathcal{M}')`
`c_xy.<x,y> = M.chart('x:(-1,1) y:(-1,1)', coord_restrictions=lambda x,y:
x^2+y^2<1)`
`g = M.riemannian_metric('g')`
`g[0,0], g[1,1] = 4/(1 - x^2 - y^2)^2, 4/(1 - x^2 - y^2)^2`
`e1 = M.vector_field((1 - x^2 - y^2) / 2, 0)`
`e2 = M.vector_field(0, (1 - x^2 - y^2) / 2)`
`e = M.vector_frame('e', (e1, e2), non_coordinate_basis=True)`
`nabla = g.connection()`
`omega = nabla.connection_form`
`omega(0,0).display(e), omega(0,1).display(e)`
> (nabla_g connection 1-form (0,0) = x e^0 + y e^1,
> nabla_g connection 1-form (0,1) = y e^0 - x e^1)
`omega(1,0).display(e), omega(0,1).display(e)`
> (nabla_g connection 1-form (1,0) = -y e^0 + x e^1,
> nabla_g connection 1-form (0,1) = y e^0 - x e^1)
--
You received this message because you are subscribed to the Google Groups
"sage-support" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To view this discussion on the web visit
https://groups.google.com/d/msgid/sage-support/817ba4d5-5482-45ad-a704-cdf5f19d0cb0n%40googlegroups.com.
