Geodesic
Integrability properties of $NC_{10}$-manifolds
Matematičeskaâ fizika i kompʹûternoe modelirovanie, Tome 20 (2017) no. 5, pp. 32-38.

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

In this paper we investigate the integrability properties of $NC_{10}$-manifolds. In particular, it is shown that the integrable $NC_{10}$-structure, and also the normal $NC_{10}$-structure, is cosymplectic. It is shown that $NC_{10}$-structure with a closed contact form is finer than cosymplectic. Local structures of investigated manifolds are given.
Keywords: cosymplectic structure, integrable structure, approximately Kähler manifold, finitely cosymplectic structure, Nijenhuis tensor, $NC_{10}$-manifold.
Mots-clés : normal structure 
@article{VVGUM_2017_20_5_a3,
     author = {A. R. Rustanov},
     title = {Integrability properties of $NC_{10}$-manifolds},
     journal = {Matemati\v{c}eska\^a fizika i kompʹ\^uternoe modelirovanie},
     pages = {32--38},
     publisher = {mathdoc},
     volume = {20},
     number = {5},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VVGUM_2017_20_5_a3/}
}
TY  - JOUR
AU  - A. R. Rustanov
TI  - Integrability properties of $NC_{10}$-manifolds
JO  - Matematičeskaâ fizika i kompʹûternoe modelirovanie
PY  - 2017
SP  - 32
EP  - 38
VL  - 20
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VVGUM_2017_20_5_a3/
LA  - ru
ID  - VVGUM_2017_20_5_a3
ER  - 
%0 Journal Article
%A A. R. Rustanov
%T Integrability properties of $NC_{10}$-manifolds
%J Matematičeskaâ fizika i kompʹûternoe modelirovanie
%D 2017
%P 32-38
%V 20
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VVGUM_2017_20_5_a3/
%G ru
%F VVGUM_2017_20_5_a3
A. R. Rustanov. Integrability properties of $NC_{10}$-manifolds. Matematičeskaâ fizika i kompʹûternoe modelirovanie, Tome 20 (2017) no. 5, pp. 32-38. http://geodesic.mathdoc.fr/item/VVGUM_2017_20_5_a3/

[1] V. F. Kirichenko, A. R. Rustanov, “Differential Geometry of Quasi-Sasakian Manifolds”, Matematicheskiy sbornik, 193:8 (2002), 71–100 | DOI

[2] V. F. Kirichenko, Differential-Geometric Structures on Manifolds, Pechatnyy dom, Odessa, 2013, 495 pp.

[3] A. R. Rustanov, “$NC_{10}$-Manifolds”, Prepodavatel XXI veka, 2014, no. 3, 209–218

[4] A. R. Rustanov, S. V. Kharitonova, “$NC_{10}$-Manifolds of $R_1$ Class”, Vestnik Adygeyskogo gosudarstvennogo universiteta. Seriya «estestvenno-matematicheskie i tekhnicheskie nauki», 2016, no. 2, 48–54

[5] A. R. Rustanov, “$NC_{10}$-Manifolds of $R_2$ Class”, Vestnik Adygeyskogo gosudarstvennogo universiteta. Seriya «estestvenno-matematicheskie i tekhnicheskie nauki», 2016, no. 4, 43–48

[6] D. E. Blair, Contact manifolds in Riemannian geometry, Lect. Notes in Math, 509, 1976, 146 pp. | DOI | MR

[7] S. Sasaki, J. Hatakeyama, “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