Osaka Journal of Mathematics

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

Domenico Perrone

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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

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1221656644

Mathematical Reviews number (MathSciNet)
MR2468585

Zentralblatt MATH identifier
1155.53027

Subjects
Primary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)
Secondary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.) 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20] 53D10: Contact manifolds, general

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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