Some properties of homogeneous \(\mathcal{E}\)-manifolds (Q2037719)

In [Izv. Math. 83, No. 1, 20--48 (2019; Zbl 1412.30139); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 83, No. 1, 25--85 (2019)] the author introduced the notion of an \(\mathcal{E}\)-structure on a homogeneous space \(G/H\). These structures generalize the dual structure based on the notion of dual numbers. Some corrections on this paper appeared in reference [the author, ``Corrections and additions to my article `Dual and almost-dual homogeneous spaces' '', Preprint, \url{arXiv:2007.14303}], and in the present paper they are presented in more detail. He also studies \(\mathcal{E}\)-homogeneous spaces of low dimension. In particular, he refines the assertions of [loc. cit.] concerning these spaces. Together with homogeneous spaces themselves, he also considers geometric questions related to \(\mathcal{E}\)-homogeneous spaces by Klein's Erlangen Program.