Classification of compact homogeneous spaces with invariant G _2-structures

摘要

In this note we classify all homogeneous spaces G/H admitting a G-invariant G _2- structure, assuming that G is a connected compact Lie group and G acts effectively on G/H. They include a subclass of all homogeneous spaces G/H with a G-invariant G? _2-structure, where G is a compact Lie group. There are many new examples with nontrivial fundamental group. We study a subclass of homogeneous spaces of high rigidity and low rigidity and show that they admit families of invariant coclosed G _2-structures (respectively G? _2-structures).