Killing Mean Curvature Solitons from Riemannian Submersions

TL;DR

This paper introduces a novel method to construct mean curvature solitons on manifolds with Killing vector fields, utilizing Riemannian submersions to simplify PDEs to ODEs, leading to new hyperbolic space examples.

Contribution

It develops a general construction technique for mean curvature solitons using Riemannian submersions and Killing fields, providing new explicit examples in hyperbolic space.

Findings

New examples of mean curvature solitons in hyperbolic space

Reduction of PDEs to ODEs via Riemannian submersion techniques

Construction of rotator solutions in specific geometric settings

Abstract

We present a new general construction of examples of mean curvature solitons on manifolds admitting a nowhere-vanishing Killing vector field. Using Riemannian submersion techniques, we reduce the problem from a PDE to an ODE. As an application, we obtain new examples of rotators in hyperbolic space.