  The 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.
