In this paper 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).
Publié le : 2008-09-15
Classification:
53C25,
53C15,
53C20,
53D10
@article{1221656644,
author = {Perrone, Domenico},
title = {Corrected energy of the Reeb distribution of a 3-Sasakian manifold},
journal = {Osaka J. Math.},
volume = {45},
number = {1},
year = {2008},
pages = { 615-627},
language = {en},
url = {http://dml.mathdoc.fr/item/1221656644}
}
Perrone, Domenico. Corrected energy of the Reeb distribution of a 3-Sasakian manifold. Osaka J. Math., Tome 45 (2008) no. 1, pp. 615-627. http://gdmltest.u-ga.fr/item/1221656644/