Classification of five-dimensional naturally reductive spaces. (English) Zbl 0555.53024

A general conjecture suggested by the authors says that, on a naturally reductive homogeneous Riemannian space, (M,g), every two I(M)-invariant differential operators commute. This conjecture was proved earlier for dimensions 3 and 4 by the same authors. The aim of the present paper is to prove the conjecture for dimension five via the explicit classification. (An interesting feature of the classification itself is that the most general classes depend on several real parameters and one rational parameter.)


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