The torsion flow on a closed pseudohermitian 3-manifold

2013/05/23 by Shu-Cheng Chang, Chang, Shu-Cheng, Otto van Koert +3
Mathematics · Physics and Astronomy · #32G07 #53C21 #53D35 #Advanced Differential Geometry Research #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Symplectic Geometry (math.SG) #math.CV #math.DG #math.SG #msc:32G07 #msc:53C21 #msc:53D35

paper · pdf · doi:10.48550/arxiv.1305.5391

The short-time existence proof from v1 contained a mistake. The corrected existence results only hold for a special class of CR structures

openalex publication_date 2013/05/23 · arxiv created 2014/01/22 · arxiv updated 2014/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we define the torsion flow, a CR analogue of the Ricci flow. For homogeneous CR manifolds we give explicit solutions to the torsion flow illustrating various kinds of behavior. We also derive monotonicity formulas for CR entropy functionals. As an application, we classify torsion breathers.

Related

• Short-Time Existence Theorem for the CR Torsion Flow
• Evolution of the Torsional Rigidity under Geometric Flows
• C₀-positivity and a classification of closed three-dimensional CR torsion solitons
• A characterization of homogeneous three-dimensional CR manifolds
• Ricci flow on three-dimensional manifolds with symmetry