By a recent result, it is known that compact homogeneous spaces with co-index of symmetry 4 are quotients of a semisimple Lie group of dimension at most 10. In this paper we determine exactly which ones of these spaces actually admit such a metric. For all the admissible spaces we construct explicit examples of these metrics.
Covering maps and ideal embeddings of compact homogeneous spaces
A global view of equivariant vector bundles and Dirac operators on some compact homogeneous spaces
Semisimple Weakly Symmetric Pseudo--Riemannian Manifolds
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