Geodesic
Hermitian $f$-structures on $6$-dimensional filiform Lie groups
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2016), pp. 34-43.

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider left-invariant $f$-structures on $6$-dimensional filiform Lie groups. We indicate some sufficient conditions under which the special left-invariant $f$-structures on these Lie groups belong to the class of Hermitian $f$-structures. We also present particular examples of the corresponding $f$-structures.
Keywords: metric $f$-structure, left-invariant $f$-structure, the Levi-Civita connection, nilpotent Lie algebra, Hermitian $f$-structure
Mots-clés : filiform Lie group. 
@article{IVM_2016_7_a4,
     author = {P. A. Dubovik},
     title = {Hermitian $f$-structures on $6$-dimensional filiform {Lie} groups},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {34--43},
     publisher = {mathdoc},
     number = {7},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2016_7_a4/}
}
TY  - JOUR
AU  - P. A. Dubovik
TI  - Hermitian $f$-structures on $6$-dimensional filiform Lie groups
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2016
SP  - 34
EP  - 43
IS  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2016_7_a4/
LA  - ru
ID  - IVM_2016_7_a4
ER  - 
%0 Journal Article
%A P. A. Dubovik
%T Hermitian $f$-structures on $6$-dimensional filiform Lie groups
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2016
%P 34-43
%N 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2016_7_a4/
%G ru
%F IVM_2016_7_a4
P. A. Dubovik. Hermitian $f$-structures on $6$-dimensional filiform Lie groups. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2016), pp. 34-43. http://geodesic.mathdoc.fr/item/IVM_2016_7_a4/

[1] Balaschenko V. V., Nikonorov Yu. G., Rodionov E. D., Slavskii V. V., Odnorodnye prostranstva: teoriya i prilozheniya, Poligrafist, Khanty-Mansiisk, 2008

[2] Yano K., “On a structure defined by a tensor field $f$ of type $(1,1)$ satisfying $f^3+f=0$”, Tensor, 14 (1963), 99–109 | MR | Zbl

[3] Kirichenko V. F., “Metody obobschennoi ermitovoi geometrii v teorii pochti kontaktnykh mnogoobrazii”, Itogi nauki i tekhn. Probl. geometrii, 18, VINITI AN SSSR, 1986, 25–71 | MR | Zbl

[4] Stepanov N. A., “Osnovnye fakty teorii $\varphi$-prostranstv”, Izv. vuzov. Matem., 1967, no. 3, 88–95 | MR | Zbl

[5] Fedenko A. S., Prostranstva s simmetriyami, Izd-vo Belorusskogo un-ta, Minsk, 1977 | MR

[6] Kovalskii O., Obobschennye simmetricheskie prostranstva, Mir, M., 1984 | MR

[7] Balaschenko V. V., Stepanov N. A., “Kanonicheskie affinornye struktury klassicheskogo tipa na regulyarnykh $\Phi$-prostranstvakh”, Matem. sb., 186:11 (1995), 3–34 | MR | Zbl

[8] Balaschenko V. V., “Kanonicheskie $f$-struktury giperbolicheskogo tipa na regulyarnykh $\Phi$-prostranstvakh”, UMN, 53:4 (1998), 213–214 | DOI | MR | Zbl

[9] Kaplan A., “Riemannian nilmanifolds attached to Clifford modules”, Geom. Dedicata, 11:2 (1981), 127–136 | DOI | MR | Zbl

[10] Kaplan A., “On the geometry of groups of Heisenberg type”, Bull. London Math. Soc., 15:1 (1983), 35–42 | DOI | MR | Zbl

[11] Balashchenko V. V., “Invariant structures on the $6$-dimensional generalized Heisenberg group”, Kragujevac J. Math., 35:2 (2011), 209–222 | MR | Zbl

[12] Balaschenko V. V., Dubovik P. A., “Levoinvariantnye $f$-struktury na $5$-mernoi gruppe Geizenberga $H(2,1)$”, Vestn. BGU. Ser. 1. Matem. Fiz. Inform., 2013, no. 3, 112–117

[13] Balaschenko V. V., “Odnorodnye ermitovy $f$-mnogoobraziya”, UMN, 56:3 (2001), 159–160 | DOI | MR | Zbl

[14] Yano K., Kon M., $CR$-podmnogoobraziya v kelerovom i sasakievom mnogoobraziyakh, Nauka, M., 1990 | MR | Zbl

[15] Kirichenko V. F., “Kvaziodnorodnye mnogoobraziya i obobschennye pochti ermitovy struktury”, Izv. AN SSSR. Ser. matem., 47:6 (1983), 1208–1223 | MR | Zbl

[16] Khelgason S., Differentsialnaya geometriya i simmetricheskie prostranstva, Mir, M., 1964

[17] Kobayasi Sh., Nomidzu K., Osnovy differentsialnoi geometrii, v. 2, Nauka, M., 1981

[18] Khakimdjanov Yu., Goze M., Medina A., “Sympletic or contact structures on Lie groups”, Differential Geometry Appl., 21:1 (2004), 41–54 | DOI | MR | Zbl

[19] Vergne M., “Cohomologie des algèbres de Lie nilpotentes. Application à l'étude de la variété des algèbres de Lie nilpotentes”, Bull. Soc. Math. France, 98:1 (1970), 81–116 | MR | Zbl

[20] Morozov V. V., “Klassifikatsiya nilpotentnykh algebr Li shestogo poryadka”, Izv. vuzov. Matem., 1958, no. 4, 161–171 | MR | Zbl