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

Der Chen Chang; Shu Cheng Chang; Ting Jung Kuo; Chien Lin

doi:10.4310/PAMQ.2022.v18.n2.a3

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

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

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

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 3manifold of the nonnegative CR Paneitz operator with a kernel consisting of the CR pluriharmonic functions and the CR Q-curvature is pluriharmonic.

Original language	English
Pages (from-to)	411-436
Number of pages	26
Journal	Pure and Applied Mathematics Quarterly
Volume	18
Issue number	2
DOIs	https://doi.org/10.4310/PAMQ.2022.v18.n2.a3
Publication status	Published - 2022

Keywords

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

ASJC Scopus subject areas

General Mathematics

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10.4310/PAMQ.2022.v18.n2.a3

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title = "Vanishing theorem of Kohn-Rossi cohomology class and rigidity of Sasakian space form",

abstract = "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 3manifold of the nonnegative CR Paneitz operator with a kernel consisting of the CR pluriharmonic functions and the CR Q-curvature is pluriharmonic.",

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

author = "Chang, \{Der Chen\} and Chang, \{Shu Cheng\} and Kuo, \{Ting Jung\} and Chien Lin",

year = "2022",

doi = "10.4310/PAMQ.2022.v18.n2.a3",

language = "English",

volume = "18",

pages = "411--436",

journal = "Pure and Applied Mathematics Quarterly",

issn = "1558-8599",

publisher = "International Press of Boston, Inc.",

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}

TY - JOUR

T1 - Vanishing theorem of Kohn-Rossi cohomology class and rigidity of Sasakian space form

AU - Chang, Der Chen

AU - Chang, Shu Cheng

AU - Kuo, Ting Jung

AU - Lin, Chien

PY - 2022

Y1 - 2022

N2 - 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 3manifold of the nonnegative CR Paneitz operator with a kernel consisting of the CR pluriharmonic functions and the CR Q-curvature is pluriharmonic.

AB - 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 3manifold of the nonnegative CR Paneitz operator with a kernel consisting of the CR pluriharmonic functions and the CR Q-curvature is pluriharmonic.

KW - CR Paneitz operator

KW - CR Q-curvature

KW - CR pluriharmonic operator

KW - CR rigidity theorem

KW - Pseudo-Einstein

KW - Sasakian manifold

KW - Sasakian space form

KW - Tangential Cauchy-Riemann equation

UR - https://www.scopus.com/pages/publications/85131194646

UR - https://www.scopus.com/pages/publications/85131194646#tab=citedBy

U2 - 10.4310/PAMQ.2022.v18.n2.a3

DO - 10.4310/PAMQ.2022.v18.n2.a3

M3 - Article

AN - SCOPUS:85131194646

SN - 1558-8599

VL - 18

SP - 411

EP - 436

JO - Pure and Applied Mathematics Quarterly

JF - Pure and Applied Mathematics Quarterly

IS - 2

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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