Geodesic
On the geometry of holomorphic torse-forming vector fields on almost contact metric manifolds
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 3, Tome 222 (2023), pp. 83-93.

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

Several new results on holomorphic torse-forming vector fields on almost contact metric manifolds are obtained.
Keywords: torse-forming vector field, holomorphic torse-forming vector field, special concircular vector field, almost contact metric manifold
Mots-clés : $\xi$-invariant structure. 
@article{INTO_2023_222_a7,
     author = {A. R. Rustanov and O. E. Arsen'eva and S. V. Kharitonova},
     title = {On the geometry of holomorphic torse-forming vector fields on almost contact metric manifolds},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {83--93},
     publisher = {mathdoc},
     volume = {222},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2023_222_a7/}
}
TY  - JOUR
AU  - A. R. Rustanov
AU  - O. E. Arsen'eva
AU  - S. V. Kharitonova
TI  - On the geometry of holomorphic torse-forming vector fields on almost contact metric manifolds
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2023
SP  - 83
EP  - 93
VL  - 222
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2023_222_a7/
LA  - ru
ID  - INTO_2023_222_a7
ER  - 
%0 Journal Article
%A A. R. Rustanov
%A O. E. Arsen'eva
%A S. V. Kharitonova
%T On the geometry of holomorphic torse-forming vector fields on almost contact metric manifolds
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2023
%P 83-93
%V 222
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2023_222_a7/
%G ru
%F INTO_2023_222_a7
A. R. Rustanov; O. E. Arsen'eva; S. V. Kharitonova. On the geometry of holomorphic torse-forming vector fields on almost contact metric manifolds. 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 3, Tome 222 (2023), pp. 83-93. http://geodesic.mathdoc.fr/item/INTO_2023_222_a7/

[1] Abu-Saleem A., Rustanov A. R., Kharitonova S. V., “Svoistva integriruemosti obobschennykh mnogoobrazii Kenmotsu”, Vladikavk. mat. zh., 20:3 (2018), 4–20

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

[3] Kirichenko V. F., “O geometrii priblizhenno sasakievykh mnogoobrazii”, Dokl. AN SSSR., 269:1 (1983), 24–29

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

[5] Kirichenko V. F., Kuzakon V. M., “O geometrii golomorfnykh torsoobrazuyuschikh vektornykh polei na pochti ermitovykh mnogoobraziyakh”, Ukr. mat. zh., 65:7 (2013), 1005–1008

[6] Kirichenko V. F., Kusova E. V., “O geometrii slabo kosimplekticheskikh mnogoobrazii”, Fundam. prikl. mat., 16:2 (2010), 33–42

[7] Kirichenko V. F., Terpstra M. A., “O geometrii kharakteristicheskogo vektora $lcQS$-mnogoobraziya”, Mat. zametki., 92:6 (2012), 864–871

[8] Kruchkov G. I., “Ob odnom klasse rimanovykh prostranstv”, Tr. semin. vekt. tenz. anal., 1961, no. 1, 103–128

[9] Kuzakon V. M., “O golomorfnosti torsoobrazuyuschikh vektornykh polei na pochti ermitovykh mnogoobraziyakh”, Ukr. mat. zh., 67:3 (2015), 420–430

[10] Mikesh I., O kontsirkulyarnykh vektornykh polyakh «v tselom» na kompaktnykh rimanovykh prostranstvakh, Dep. v Ukr. NIINTI 02.03.88. — No 615-Uk88., Odessa

[11] 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

[12] Shirokov P. A., “O skhodyaschikhsya napravleniyakh v rimanovykh prostranstvakh”, Izv. fiz.-mat. o-va., 1934/35, no. 7, 77–88

[13] Fijii M., “Some Riemannian manifolds admitting a concircular scalar field”, Math. J. Okayama Univ., 16:1 (1973), 1–9

[14] Goldberg S., Yano K., “Integrability of almost cosymplectic structures”, Pac. J. Math., 31:2 (1969), 373–382

[15] Kenmotsy K., “A class of almost contact Riemannian manifolds”, Tôhoku Math. J., 24:1 (1972), 93–103

[16] Kim In-Bae., “Special concircular vector fields in Riemannian manifolds”, Hiroshima Math. J., 12:1 (1982), 77–91

[17] Koyanagi T., “On a certain property of a Riemannian space admitting a special concircular scalar field”, J. Fac. Sci. Hokkaido Univ., 22:3, 4 (1972), 154–157

[18] Takeno H., “Concircular scalar field in spherically symmetric spacetime, I”, Tensor, N.S., 20:2 (1969), 167–176

[19] Tandai K., “Riemannian manifold admitting more than $n-1$ linearly independent solutions of $\nabla^2\rho+c^2\rho g=0$”, Hokkaido Math. J., 1:1 (1972), 12–15

[20] Yano K., “Concircular geometry, I–IV”, Proc. Imp. Acad. Jpn., 16:6 (1940), 195–200, 354–360, 442–448, 505–511