Abstract
This chapter focuses on homogeneous Einstein metrics on certain Kähler C-spaces. Most known nonstandard examples of compact homogeneous Einstein manifolds are constructed via Riemannian submersions. The word “standard” implies that the Einstein metric on a homogeneous manifold is constructed from the irreducible isotropy representation of the homogeneous manifold. However, such a method does not work effectively if the isotropy representation associated with the homogeneous manifold decomposes into more than two irreducible representations.
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