Invariant $f$-structures on naturally reductive homogeneous spaces
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2008), pp. 3-15
Voir la notice de l'article provenant de la source Math-Net.Ru
We study invariant metric $f$-structures on naturally reductive homogeneous spaces and establish their relation to generalized Hermitian geometry. We prove a series of criteria characterizing geometric and algebraic properties of important classes of metric $f$-structures: nearly Kähler, Hermitian, Kähler, and Killing structures. It is shown that canonical $f$-structures on homogeneous $\Phi$-spaces of order $k$ (homogeneous $k$-symmetric spaces) play remarkable part in this line of investigation. In particular, we present the final results concerning canonical $f$-structures on naturally reductive homogeneous $\Phi$-spaces of order 4 and 5.
Keywords:
naturally reductive space - invariant $f$-structure - generalized Hermitian geometry, homogeneous $\Phi$-space, homogeneous $k$-symmetric space, canonical $f$-structure.
@article{IVM_2008_4_a0,
author = {V. V. Balashchenko},
title = {Invariant $f$-structures on naturally reductive homogeneous spaces},
journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
pages = {3--15},
publisher = {mathdoc},
number = {4},
year = {2008},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/IVM_2008_4_a0/}
}
V. V. Balashchenko. Invariant $f$-structures on naturally reductive homogeneous spaces. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2008), pp. 3-15. http://geodesic.mathdoc.fr/item/IVM_2008_4_a0/