Geodesic
On the Geometry of the Characteristic Vector of an~$\mathit{lcQS}$-Manifold
Matematičeskie zametki, Tome 92 (2012) no. 6, pp. 864-871.

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

We study conditions under which the characteristic vector of a normal $\mathit{lcQS}$-manifold is a torsion-forming or even a concircular vector field. We prove that the following assertions are equivalent: an $\mathit{lcQS}$-structure is normal, and its characteristic vector is a torsion-forming vector field; an $\mathit{lcQS}$-structure is normal, and its characteristic vector is a concircular vector field; an $\mathit{lcQS}$-structure is locally conformally cosymplectic and has a closed contact form.
Keywords: Sasakian structure, Riemannian manifold, contact form characteristic vector, concircular vector field, torsion-forming vector field.
Mots-clés : $\mathit{AC}$-structure, $\mathit{lcQS}$-structure 
@article{MZM_2012_92_6_a6,
     author = {V. F. Kirichenko and M. A. Terpstra},
     title = {On the {Geometry} of the {Characteristic} {Vector} of an~$\mathit{lcQS}${-Manifold}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {864--871},
     publisher = {mathdoc},
     volume = {92},
     number = {6},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_92_6_a6/}
}
TY  - JOUR
AU  - V. F. Kirichenko
AU  - M. A. Terpstra
TI  - On the Geometry of the Characteristic Vector of an~$\mathit{lcQS}$-Manifold
JO  - Matematičeskie zametki
PY  - 2012
SP  - 864
EP  - 871
VL  - 92
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2012_92_6_a6/
LA  - ru
ID  - MZM_2012_92_6_a6
ER  - 
%0 Journal Article
%A V. F. Kirichenko
%A M. A. Terpstra
%T On the Geometry of the Characteristic Vector of an~$\mathit{lcQS}$-Manifold
%J Matematičeskie zametki
%D 2012
%P 864-871
%V 92
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2012_92_6_a6/
%G ru
%F MZM_2012_92_6_a6
V. F. Kirichenko; M. A. Terpstra. On the Geometry of the Characteristic Vector of an~$\mathit{lcQS}$-Manifold. Matematičeskie zametki, Tome 92 (2012) no. 6, pp. 864-871. http://geodesic.mathdoc.fr/item/MZM_2012_92_6_a6/

[1] S. S. Chern, “Pseudo-groupes continus infinis”, Géométrie Différentielle, Colloq. Internat. CNRS, 52, Centre National de la Recherche Scientifique, Paris, 1953, 119–136 | MR | Zbl

[2] J. W. Gray, Contact structures, Abst. Short Communs Internat. Congress Math. in Edinburgh, Univ. Edinburgh, Edinburgh, 1958

[3] J. W. Gray, “Some global properties of contact structures”, Ann. of Math. (2), 69:2 (1959), 421–450 | DOI | MR | Zbl

[4] S. Sasaki, “On differentiable manifolds with certain structures which are closely related to almost contact structure. I”, Tôhoku Math. J. (2), 12:3 (1960), 459–476 ; S. Sasaki, Y. Hatakeyama, “On differentiable manifolds with certain structures which are closely related to almost contact structure. II”, Tôhoku Math. J. (2), 13:2 (1961), 281–294 | DOI | MR | Zbl | DOI | MR | Zbl

[5] Z. Olszak, “Locally conformal almost cosymplectic manifolds”, Colloq. Math., 57:1 (1989), 73–87 | MR | Zbl

[6] V. F. Kirichenko, N. S. Baklashova, “Geometriya kontaktnoi formy Li i kontaktnyi analog teoremy Ikuty”, Matem. zametki, 82:3 (2007), 347–360 | DOI | MR | Zbl

[7] V. F. Kirichenko, E. A. Polkina, “Geodezicheskaya zhestkost nekotorykh klassov pochti kontaktnykh metricheskikh mnogoobrazii”, Izv. vuzov. Matem., 2007, no. 9, 42–49 | MR | Zbl

[8] D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, Progr. Math., 203, Birkhäuser Boston, Boston, 2002 | MR | Zbl

[9] V. F. Kirichenko, “O geometrii mnogoobrazii Kenmotsu”, DAN, 380:5 (2001), 585–587 | MR | Zbl

[10] V. F. Kirichenko, “Differentsialnaya geometriya glavnykh toroidalnykh rassloenii”, Fundament. i prikl. matem., 6:4 (2000), 1095–1120 | MR | Zbl

[11] V. F. Kirichenko, Differentsialno-geometricheskie struktury na mnogoobraziyakh, MPGU, M., 2003

[12] D. E. Blair, Contact Manifolds in Riemannian Geometry, Lecture Notes in Math., 509, Springer-Verlag, Berlin, 1976 | DOI | MR | Zbl

[13] A. V. Aminova, Proektivnye preobrazovaniya psevdorimanovykh mnogoobrazii, Yanus-K, M., 2003