A 4-hyperboloid has negative curvature, with
(1)
|
(2)
|
Since
(3)
|
it follows that
(4)
|
To stay on the surface of the hyperboloid, the line element is given by
(5)
| |||
(6)
| |||
(7)
|
A 4-hyperboloid has negative curvature, with
(1)
|
(2)
|
Since
(3)
|
it follows that
(4)
|
To stay on the surface of the hyperboloid, the line element is given by
(5)
| |||
(6)
| |||
(7)
|
Weisstein, Eric W. "Hyperboloid Embedding." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HyperboloidEmbedding.html