# June 10, 2010 Afternoon reading

..we show that the Reeb distribution on a spherical space form which admits a 3-Sasakian structure minimizes the corrected energy. Analogously for the characteristic distribution of the normal complex contact structure on the complex projective space $\mathbb {C}P^{2m+1}$ induced via the Hopf fibration $S^{1}\hookrightarrow S^ {4m+3}\to \mathbb{C}P^{2m+1}$.

This last result is a consequence of a more general result on the corrected energy of the characteristic distribution of a compact twistor space over a quaternionic-Kähler manifold with positive scalar curvature (equipped with a normal complex contact metric structure).