Geodesic
Invariant $f$-structures on naturally reductive homogeneous spaces
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2008), pp. 3-15

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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/}
}
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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/