## Osaka Journal of Mathematics

### Corrected energy of the Reeb distribution of a 3-Sasakian manifold

Domenico Perrone

#### Abstract

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).

#### Article information

Source
Osaka J. Math., Volume 45, Number 3 (2008), 615-627.

Dates
First available in Project Euclid: 17 September 2008

https://projecteuclid.org/euclid.ojm/1221656644

Mathematical Reviews number (MathSciNet)
MR2468585

Zentralblatt MATH identifier
1155.53027

#### Citation

Perrone, Domenico. Corrected energy of the Reeb distribution of a 3-Sasakian manifold. Osaka J. Math. 45 (2008), no. 3, 615--627. https://projecteuclid.org/euclid.ojm/1221656644

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