Transverse \mathcal F^T-entropy and transverse Ricci flow for Riemannian foliations

2021/04/22 by Dexie Lin, Lin, Dexie
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2104.10945

openalex publication_date 2021/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce an entropy functional on Riemannian foliation, inspired by the work of , which is monotonically along the transverse Ricci flow. We relate their gradient flow, via diffeomorphism preserving the foliated structure of the manifold with Riemannian foliation, to the transverse Ricci flow. Moreover, inspired by the work of Fuquan Fang and Yuhao Zhang, we give a necessary condition for codimension 4 Riemannian foliation admitting the transverse Einstein metric.

Related

• The Transverse Entropy Functional and the Sasaki-Ricci Flow
• Entropy of foliations with leafwise Finsler structure
• The entropy formula for the Ricci flow and its geometric applications
• The transverse Chern-Ricci flow
• Transverse Ricci solitons on a compact foliated manifold