On a new family of homogeneous Einstein manifolds. (English) Zbl 0787.53037

Rodionov, E. D.

Arch. Math., Brno 28, No. 3-4, 199-204 (1992).

The author studies the homogeneous spaces \(M^{2S+1}\) which appear as underlying manifolds of certain Sasakian spaces. (All of them are circle bundles over the Hermitian symmetric spaces of the form \(\mathbb{C} P^ 1(\lambda_ 1)\times \cdots\times \mathbb{C} P^ 1(\lambda_ S)\), where the holomorphic curvatures \(\lambda_ 1,\dots,\lambda_ S\) are subjected to some “rationality conditions”.) He proves that each space \(M^{2S+1}\) admits exactly one homothety class of invariant Einstein metrics, which are always different from the canonical metric of the corresponding Sasakian space.

Reviewer: O.Kowalski (Praha)

MSC:

53C25	Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C30	Differential geometry of homogeneous manifolds

Keywords:

Sasakian spaces; invariant Einstein metrics