2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/99814The Willmore energy for Frenet curves in quaternionic projective space is the generalization of the Willmore functional for immersions into the 4-sphere. Critical points of the Willmore energy are called Willmore curves in quaternionic projective space. Using a Baecklund transformation on Willmore curves, we generalize Bryant's result on Willmore spheres in 3--space: a Willmore sphere in quaternionic projective space has integer Willmore energy, and is given by complex holomorphic data.23 pages, v2: improved presentation, qualified references addedDifferential GeometryAlgebraic Geometry53Axx, 53Cxx, 30Fxxtext