- #1
Sorento7
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We know that a Clifford torus is parameterized in 4D euclidean space by:
(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?
(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?