Swimming in curved space or The Baron and the cat

TL;DR

This paper investigates how deformable bodies can swim in static curved spaces, revealing that their movement depends on the space's curvature and the swimmer's shape, with implications for understanding locomotion in curved geometries.

Contribution

It introduces a geometric framework for swimming in curved spaces and derives how curvature influences swimming distance for small deformable bodies.

Findings

Swimming distance is proportional to Riemann curvature and swimmer's moments.

The equations governing swimming are geometric in nature.

Small swimmers' motion depends on ambient space curvature.

Abstract

We study the swimming of non-relativistic deformable bodies in (empty) static curved spaces. We focus on the case where the ambient geometry allows for rigid body motions. In this case the swimming equations turn out to be geometric. For a small swimmer, the swimming distance in one stroke is determined by the Riemann curvature times certain moments of the swimmer.