On characterization for a class of pseudo-convex domains with positive constant pseudo-scalar curvature on their boundaries

For any compact strictly pseudoconvex pseudo-Hermitian CR manifold$(M, \theta_0)$ in the sense of Webster, the solution of CR-Yamabeproblem concludes that there is a contact form $\theta$ whichconformally equivalent to $\theta_0$ so that the psudo scalarcurvature for $(M, \theta)$ is a constant. The current article givesa natural and easily verified sufficient condition, and proves thatif $(M,\theta)$ satisfies the condition and has a positive constantpseudo scalar curvature on $M$, then $(M, \theta)$ must be CRequivalent to the unit sphere.

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Published 1 January 2009