Pure and Applied Mathematics Quarterly
Volume 18 (2022)
Special issue in honor of Joseph J. Kohn on the occasion of his 90th birthday
Guest Editors: J.E. Fornaess, Stanislaw Janeczko, Duong H. Phong, and Stephen S.T. Yau
Vanishing theorem of Kohn–Rossi cohomology class and rigidity of Sasakian space form
Pages: 411 – 436
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.
pseudo-Einstein, CR pluriharmonic operator, CR Paneitz operator, CR Q-curvature, tangential Cauchy–Riemann equation, Sasakian manifold, CR rigidity theorem, Sasakian space form
2010 Mathematics Subject Classification
Primary 32V05, 32V20. Secondary 53C56.
Der-Chen Chang is partially supported by an NSF grant DMS-1408839 and a McDevitt Endowment Fund at Georgetown University.
Shu-Cheng Chang and Ting-Jung Kuo are partially supported in part by the MOST of Taiwan.
Received 7 November 2020
Accepted 19 January 2021
Published 13 May 2022