Vanishing theorem of Kohn-Rossi cohomology class and rigidity of Sasakian space form

Der-Chen Chang,Shu-Cheng Chang,Ting-Jung Kuo,Chien Lin

PURE AND APPLIED MATHEMATICS QUARTERLY（2022）

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摘要

In this note, under the positivity assumption of the pseudohermitian curvature, we derive the existence theorem for pseudo-Einstein contact forms and rigidity theorems for Sasakian space forms in a closed spherical strictly pseudoconvex CR 3-manifold of the nonnegative CR Paneitz operator with a kernel consisting of the CR pluriharmonic functions and the CR Q-curvature is pluriharmonic.

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关键词

Pseudo-Einstein, CR pluriharmonic operator, CR Paneitz operator, CR Q-curvature, Tangential Cauchy-Riemann equation, Sasakian manifold, CR rigidity theorem, Sasakian space form

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