Geodesic
Integral manifolds of the first fundamental distribution $lcAC_S$-structure
Čebyševskij sbornik, Tome 23 (2022) no. 1, pp. 142-152.

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

In paper we consider aspects of the Hermitian geometry of $lcAC_S$structures. The effect of the vanishing of the Neyenhuis tensor and the associated tensors $N^{(1)}$, $N^{(2)}$, $N^{(3)}$, $N^{(4)}$ on the class of almost Hermitian structure induced on the first fundamental distribution of $lcAC_S$structures is investigated. It is proved that the almost Hermitian structure induced on integral manifolds of the first fundamental distribution: $lcAC_S $-manifolds is a structure of the class $W_2\oplus W_4$, and it will be almost Kähler if and only if $grad \ \sigma \subset L(\xi)$; an integrable $lcAC_S $-manifold is a structure of the class $W_4$; a normal $lcAC_S$-manifold is a Kähler structure; a $lcAC_S $-manifold for which $N^{(2)} (X,Y)=0$, or $N^{(3)} (X)=0$, or $N^{(4)} (X)=0$, is an almost Kähler structure in the Gray-Herwell classification of almost Hermitian structures.
Keywords: almost contact structures, almost Hermitian structures, integrability of structures, Neyenhuis tensor, normal structures. 
@article{CHEB_2022_23_1_a10,
     author = {A. R. Rustanov and E. A. Polkina and G. V. Teplyakova},
     title = {Integral manifolds of the first fundamental distribution $lcAC_S$-structure},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {142--152},
     publisher = {mathdoc},
     volume = {23},
     number = {1},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2022_23_1_a10/}
}
TY  - JOUR
AU  - A. R. Rustanov
AU  - E. A. Polkina
AU  - G. V. Teplyakova
TI  - Integral manifolds of the first fundamental distribution $lcAC_S$-structure
JO  - Čebyševskij sbornik
PY  - 2022
SP  - 142
EP  - 152
VL  - 23
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHEB_2022_23_1_a10/
LA  - ru
ID  - CHEB_2022_23_1_a10
ER  - 
%0 Journal Article
%A A. R. Rustanov
%A E. A. Polkina
%A G. V. Teplyakova
%T Integral manifolds of the first fundamental distribution $lcAC_S$-structure
%J Čebyševskij sbornik
%D 2022
%P 142-152
%V 23
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHEB_2022_23_1_a10/
%G ru
%F CHEB_2022_23_1_a10
A. R. Rustanov; E. A. Polkina; G. V. Teplyakova. Integral manifolds of the first fundamental distribution $lcAC_S$-structure. Čebyševskij sbornik, Tome 23 (2022) no. 1, pp. 142-152. http://geodesic.mathdoc.fr/item/CHEB_2022_23_1_a10/

[1] Blair D. E., “Contact manifolds in Riemannian geometry”, Lecture Notes in Mathematics, 509, Springer-Verlag, Berlin–Heidelberg, 1976, 1–146 | DOI | MR

[2] Kirichenko V. F., “Methods of generalized Hermitian geometry in the theory of almost-contact manifolds”, J. Math. Sci., 42 (1988), 1885–1919 | DOI | MR | Zbl

[3] Kirichenko V. F., Rustanov A. R., “Differentsialnaya geometriya kvazi-sasakievykh mnogoobrazii”, Matematicheskii sbornik, 193:8 (2002), 71–100 | DOI | Zbl

[4] Kirichenko V. F., Differentsialno-geometricheskie struktury na mnogoobraziyakh, Izdanie vtoroe, dopolnennoe, «Pechatnyi dom», Odessa, 2013

[5] Vaisman I., “Conformal changes of almost contact metric manifolds”, Lecture Notes in Mathematics, 792, Berlin-Heidelberg-New-York, 1980, 435–443 | DOI | MR | Zbl

[6] Kharitonova S. V., “O geometrii lokalno konformno pochti kosimplekticheskikh mnogoobrazii”, Matematicheskie zametki, 86:1 (2009), 126–138 | DOI | MR | Zbl

[7] Uorner F., Osnovy teorii gladkikh mnogoobrazii i grupp Li, per. s angl., Mir, M., 1987 | MR

[8] Kobayashi Sh., Nomidzu K. M., Osnovy differentsialnoi geometrii, Nauka, M., 1981 | MR

[9] Sasaki S., Hatakeyama J., “On differentiable manifolds with certain structures which are closely related to almost contact structure. II”, Tohoku Math. J., 13:2 (1961), 281–294 | DOI | MR | Zbl

[10] Rustanov A. R., “Svoistva integriruemosti $NC_{10}$-mnogoobrazii”, Matematicheskaya fizika i kompyuternoe modelirovanie, 20:5 (2017), 32–38 | DOI | MR

[11] Abu-Saleem A., Rustanov A. R., Kharitonova S. V., “Svoistva integriruemosti obobschennykh mnogoobrazii Kenmotsu”, Vladikavkazskii matematicheskii zhurnal, 20:3 (2018), 4–20 | DOI | MR | Zbl