# Sphere-Ellipsoid induced metrics

Gold Member
Hello,
Suppose you have a sphere, travelling at $u = 0.99 c$ along the $x$ axis in our frame S.
I was wondering how the sphere's metric changes due to Lorentz length contraction. Obviously at the rest frame of the sphere, it will appear as a sphere. However on S the sphere will appear as an ellipsoid.

How would the induced metric transform however, so that it changes from describing a sphere to describing an ellipsoid?