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.

The full text of this article is unavailable through your IP address: 172.17.0.1

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