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Could any one give me a hint how to solve this one? Let $\Omega$ be a smoothly bounded pseudoconvex domain with nonconstant automorphism group $G$, Does $G$ contains $\mathbb{R}$?

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Phrased like an exercise, and if so, perhaps not suited for MO. If this is not an exercise, could you please give some background context, explaining why you believe the result should be true? –  Yemon Choi Jun 24 '12 at 1:43
Every compact Lie group appears as the full automorphism group of some real analytically bounded strongly pseudoconvex domain in some $\mathbb{C}^n$ so the answer is no. It is a theorem of Bedford and Dadok. –  Maharana Jun 24 '12 at 14:46
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