C -positivity and a classification of closed three-dimensional CR torsion solitons
Journal
Mathematische Zeitschrift
Journal Volume
296
Journal Issue
3-4
Pages
1065-1080
Date Issued
2020
Author(s)
Abstract
A closed CR 3-manifold is said to have C-positive pseudohermitian curvature if (W+ CTor) (X, X) > 0 for any 0 ≠ X∈ T1 , 0(M). We discover an obstruction for a closed CR 3-manifold to possess C -positive pseudohermitian curvature. We classify closed three-dimensional CR Yamabe solitons according to C-positivity for C= 1 and the potential function lies in the kernel of Paneitz operator. Moreover, we show that any closed three-dimensional CR torsion soliton must be the standard Sasakian space form. At last, we discuss the persistence of C-positivity along the CR torsion flow starting from a pseudo-Einstein contact form.
Type
journal article