Corrected energy of the Reeb distribution of a 3-Sasakian manifold. (English) Zbl 1155.53027

Perrone, Domenico

Osaka J. Math. 45, No. 3, 615-627 (2008).

In the paper under review, the author shows that the Reeb distribution on a spherical space form which admits a 3-Sasakian structure minimizes the corrected energy in the set of all integrable \(3\)-dimensional distributions. He also shows that the characteristic distribution of a compact twistor space over a quaternionic-Kähler manifold with positive scalar curvature is a minimum for the corrected energy in the set of all integrable 2-dimensional distributions \(\nu \) with curvature \(K(\nu )\leq 4\).

Reviewer: Cihan Özgür (Balikesir)

MSC:

53C25	Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C15	General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C20	Global Riemannian geometry, including pinching
53D10	Contact manifolds (general theory)

Keywords:

Sasakian manifold; corrected energy

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