The De Sitter metric
and its three isotropic forms on the hyperboloid SO(1,4)/SO(1,3)
In the De Sitter group G=SO(1,4), let us put K=SO(4), H=SO(1,3),
M=SO(3) and N the R^4 sub-group of the Iwasawa decomposition.
The restriction to hyperboloid G/H, drawn above, of the
metric on R^5, which is invariant by the action of the De Sitter
group, gives us
the three types of models of universe.
The isometric imbedding of each model of universe is carried out in this
De Sitter invariant space
R^5.
![](arcENciel.gif)
To know more, a document in postscript is available while clicking
on the tulip