Geodesic
Invariance of an almost contact metric structure of a smooth manifold with respect to the characteristic vector
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998). Moscow, November 1–4, 2021. Part 4, Tome 223 (2023), pp. 24-35.

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

In this paper, we obtain criteria for the $\Phi$-invariance and the $\eta$-invariance for almost contact metric structures and a criterion for a characteristic vector $\xi$ to be a Killing vector. We find all classes of almost contact metric structures from the Kirichenko classification that are $\Phi$-invariant, $\eta$-invariant, and $\xi$ is a Killing vector. Also, we prove that for any almost contact metric structure, $\xi$ cannot be conformal Killing vector distinct from a Killing vector.
Keywords: almost contact metric structure, infinitesimal isometry.
Mots-clés : infinitesimal conformal transformation 
@article{INTO_2023_223_a2,
     author = {L. A. Ignatochkina and A. V. Nikiforova and M. A. Terpstra},
     title = {Invariance of an almost contact metric structure of a smooth manifold with respect to the characteristic vector},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {24--35},
     publisher = {mathdoc},
     volume = {223},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2023_223_a2/}
}
TY  - JOUR
AU  - L. A. Ignatochkina
AU  - A. V. Nikiforova
AU  - M. A. Terpstra
TI  - Invariance of an almost contact metric structure of a smooth manifold with respect to the characteristic vector
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2023
SP  - 24
EP  - 35
VL  - 223
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2023_223_a2/
LA  - ru
ID  - INTO_2023_223_a2
ER  - 
%0 Journal Article
%A L. A. Ignatochkina
%A A. V. Nikiforova
%A M. A. Terpstra
%T Invariance of an almost contact metric structure of a smooth manifold with respect to the characteristic vector
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2023
%P 24-35
%V 223
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2023_223_a2/
%G ru
%F INTO_2023_223_a2
L. A. Ignatochkina; A. V. Nikiforova; M. A. Terpstra. Invariance of an almost contact metric structure of a smooth manifold with respect to the characteristic vector. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998). Moscow, November 1–4, 2021. Part 4, Tome 223 (2023), pp. 24-35. http://geodesic.mathdoc.fr/item/INTO_2023_223_a2/

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

[3] Kirichenko V. F., Differentsialno-geometricheskie struktury na mnogoobraziyakh, Pechatnyi Dom, Odessa, 2013

[4] Terpstra M. A., “Invariantnost $AC$-struktury otnositelno torsoobrazuyuschego vektora Riba”, Izv. Penzensk. gos. ped. in-ta im. V. G. Belinskogo., 2011, no. 26, 248–254

[5] Terpstra M. A., O geometrii kharakteristicheskogo vektora pochti kontaktnykh metricheskikh struktur, Diss. na soisk. uch. step. kand. fiz.-mat. nauk, MPGU, M., 2011