A sphere is rigid.
Liebmann's Theorem
See also
SphereExplore with Wolfram|Alpha
References
Gray, A. Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, p. 483 and 653-654, 1997.O'Neill, B. Elementary Differential Geometry, 2nd ed. New York: Academic Press, p. 262, 1997.Referenced on Wolfram|Alpha
Liebmann's TheoremCite this as:
Weisstein, Eric W. "Liebmann's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LiebmannsTheorem.html