C0-positivity and a classification of closed three-dimensional CR torsion solitons

被引：0

作者：

Cao, Huai-Dong ^{[1
]}

Chang, Shu-Cheng ^{[2
]}

Chen, Chih-Wei ^{[3
]}

机构：

[1] Lehigh Univ, Dept Math, Bethlehem, PA 18015 USA

[2] Natl Taiwan Univ, TIMS, Dept Math, Taipei 10617, Taiwan

[3] Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung, Taiwan

来源：

MATHEMATISCHE ZEITSCHRIFT | 2020年 / 296卷 / 3-4期

关键词：

CR Harnack quantity; CR torsion soliton; CR Paneitz operator; HARNACK INEQUALITIES; HEAT-EQUATION; YAMABE FLOW; RICCI FLOW; CURVATURE; MANIFOLDS;

D O I：

10.1007/s00209-020-02471-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A closed CR 3-manifold is said to have C0-positive pseudohermitian curvature if ( W + C0Tor)( X, X) > 0 for any 0 = X. T1,0( M). We discover an obstruction for a closed CR 3-manifold to possess C0 -positive pseudohermitian curvature. We classify closed threedimensional CR Yamabe solitons according to C0-positivity for C0 = 1 and the potential function lies in the kernel of Paneitz operator. Moreover, we show that any closed threedimensional CR torsion solitonmust be the standard Sasakian space form. At last, we discuss the persistence of C0-positivity along the CR torsion flow starting from a pseudo-Einstein contact form.

引用

页码：1065 / 1080

页数：16

共 36 条

[1]

Cao H.D., 2011, MATH RES LETT, DOI 10.4310/MRL.2012.v19.n4.a3

[2] ON HARNACK INEQUALITIES FOR THE KAHLER-RICCI FLOW [J].