Annals of Mathematical Sciences and Applications

Volume 8 (2023)

Number 1

Kohn–Rossi cohomology class, Sasakian space form and CR Frankel conjecture

Pages: 79 – 109

DOI: https://dx.doi.org/10.4310/AMSA.2023.v8.n1.a3

Authors

Der-Chen Chang (Department of Mathematics and Statistics, Georgetown University, Washington, D.C., U.S.A.; and Graduate Institute of Business Administration, College of Management, Fu Jen Catholic University, Taipei, Taiwan)

Shu-Cheng Chang (Department of Mathematics, National Taiwan University, Taipei, Taiwan; and Mathematical Science Research Center, Chongqing University of Technology, Chongqing, China)

Ting-Jung Kuo (Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan)

Chien Lin (Mathematical Science Research Center, Chongqing University of Technology, Chongqing, China)

Abstract

In this paper, we give a criterion of pseudo-Einstein contact forms and then affirm the CR analogue of Frankel conjecture in a closed, spherical, strictly pseudoconvex CR manifold of nonnegative pseudohermitian curvature on the space of smooth representatives of the first Kohn–Rossi cohomology group.

Keywords

Pseudo-Einstein, CR-pluriharmonic operator, CR Paneitz operator, CR Frankel conjecture, Spherical structure, Riemann mapping theorem. Lee conjecture, Kohn-Rossi cohomology group

2010 Mathematics Subject Classification

Primary 32V05, 32V20. Secondary 53C56.

Full Text (PDF format)

All authors contributed equally to this work which included mathematical theory and analysis. The authors have read and agreed to the published version of the manuscript.

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.

Chien Lin is partially supported by a project of the Ministry of Science and Technology of China (Grant number QN2022035003L).

Received 28 July 2022

Accepted 28 July 2022

Published 30 March 2023