Abstract:
We study the connection between the Lie bracket on the tangent space of homogeneous periodic $\Phi$-spaces and operators of canonical affinor structures of these spaces. The obtained relations allow us to indicate several cases of integrability of the mentioned structures.
This publication is cited in the following 3 articles:
A. S. Samsonov, “Nearly Kähler and Hermitian $f$-structures on homogeneous $\Phi$-spaces of order 6”, Russian Math. (Iz. VUZ), 55:4 (2011), 74–82
A. S. Samsonov, “Nearly Kähler and Hermitian $f$-structures on homogeneous $\Phi$-spaces of order $k$ with special metrics”, Siberian Math. J., 52:6 (2011), 1092–1103
Balashchenko V.V., Samsonov A.S., “Nearly Kähler and Hermitian $f$-structures on homogeneous $k$-symmetric spaces”, Dokl. Math., 81:3 (2010), 386–389