We know that a Clifford torus is parameterized in 4D euclidean space by:(adsbygoogle = window.adsbygoogle || []).push({});

(x1,x2,x3,x4) = (Sin(theta1), Cos(theta1), Sin(theta2), Cos(theta2))

{0<=theta1 and theta2<2pi}

Consider that a clifford torus is the immediate result of Circle * Circle

Now, have you encountered a similar manifold which is a result of Sphere * Sphere?

The parameterization is quite straight-forward in 6 dimensions:

(x1,x2,x3,x4,x5,x6)=(Sin(theta1)Cos(phi1), Cos(theta1)Cos(phi1), Sin(phi1), Sin(theta2)Cos(phi2), Cos(theta2)Cos(phi2), Sin(phi2))

{0<= All angles< 2pi}

Does there exist any name for this special 4D manifold?

**Physics Forums - The Fusion of Science and Community**

# Name this 4D Manifold?

Have something to add?

- Similar discussions for: Name this 4D Manifold?

Loading...

**Physics Forums - The Fusion of Science and Community**