asdkashdkjashd·vor 11 Jahren·discussOh, I see. I thought you were trying to prove something different.
asdkashdkjashd·vor 11 Jahren·discussThe correct higher-dimensional analogue replaces S^2 by the complex projective space CP^n and the height function by the corresponding moment map.
asdkashdkjashd·vor 11 Jahren·discussYou have to assume that the one-dimensional marginals are Gaussian for otherwise the statement is not correct.