Hypersurfaces in the quaternions. II (Q914169)

Let M be an orientable hypersurface in the quaternionic space \({\mathbb{H}}\) and \(\xi\) a unit normal vector field on M. By applying the imaginary units i,j,k of \({\mathbb{H}}\) to \(\xi\) one obtains three orthonormal vector fields \(\xi\) i,\(\xi\) j,\(\xi\) k on M. The author studies hypersurfaces M in \({\mathbb{H}}\) for which the integral curves of \(\xi\) i,\(\xi\) j,\(\xi\) k are geodesics in M or circles in M or \({\mathbb{H}}\).