Extrinsic geometric flows on foliated manifolds, II

TL;DR

This paper introduces soliton solutions to extrinsic geometric flows on foliated manifolds, analyzing their geometric properties in specific cases such as totally umbilical foliations and those driven by the extrinsic Ricci tensor.

Contribution

It extends the theory of extrinsic geometric flows by defining soliton solutions and exploring their geometry in special foliated structures.

Findings

Soliton solutions characterized for totally umbilical foliations

Analysis of EGF on foliations of surfaces

Study of EGF driven by extrinsic Ricci tensor

Abstract

Extrinsic Geometric Flow (EGF) for a codimension-one foliation has been recently introduced by authors as deformations of Riemannian metrics subject to quantities expressed in terms of its second fundamental form. In the paper we introduce soliton solutions to EGF and study their geometry for totally umbilical foliations, foliations on surfaces, and when the EGF is produced by the extrinsic Ricci tensor.