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This paper investigates the rate-distortion function, under a squared errordistortion $D$, for an $n$-dimensional random vector uniformly distributed onan $(n-1)$-sphere of radius $R$. First, an expression for the rate-distortionfunction is derived for any values of $n$, $D$, and $R$. Second, two types ofasymptotics with respect to the rate-distortion function of a Gaussian sourceare characterized. More specifically, these asymptotics concern thelow-distortion regime (that is, $D \to 0$) and the high-dimensional regime(that is, $n \to \infty$).

Uniform Distribution on $(n-1)$-Sphere: Rate-Distortion under Squared Error Distortion