Bifurcations of the Clifford Torus as Willmore Surfaces in Berger Spheres

Abstract

The Clifford torus in a Berger sphere with parameter $τ$ is a critical point of the Willmore functional for every $τ>0$, yielding a smooth path of Willmore surfaces. By estimating the Morse index along this path, we apply bifurcation theory to produce new symmetric Willmore tori emerging from the Clifford torus.