Let $R_{\theta}$ be a rotation of $S^2$ by an angle of $\theta$ around $x_1$-axis where $S^2=\{(x_1,x_2,x_3)\in \mathbb{R}^3: \sum_{i=1}^{3}x_i^2=1\}$
How can we write the corresponding mobius transformation of $\mathbb{P}^1$ ?
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This looks related: http://math.stackexchange.com/questions/1316488/explicit-fractional-linear-transformations-which-rotate-the-riemann-sphere-about. – Martin R Nov 19 '15 at 18:42