Voir la notice de l'article provenant de la source Math-Net.Ru
@article{INTO_2022_215_a2, author = {Zh. O. Aslonov}, title = {On the geometry of orbits of {Killing} vector fields}, journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory}, pages = {32--39}, publisher = {mathdoc}, volume = {215}, year = {2022}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/INTO_2022_215_a2/} }
TY - JOUR AU - Zh. O. Aslonov TI - On the geometry of orbits of Killing vector fields JO - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory PY - 2022 SP - 32 EP - 39 VL - 215 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/INTO_2022_215_a2/ LA - ru ID - INTO_2022_215_a2 ER -
Zh. O. Aslonov. On the geometry of orbits of Killing vector fields. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, Geometry, and Combinatorics, Tome 215 (2022), pp. 32-39. http://geodesic.mathdoc.fr/item/INTO_2022_215_a2/
[8] Arnold V. I., Obyknovennye differentsialnye uravneniya, Nauka, M., 1975
[9] Aslonov Zh. O., “Geometriya orbit vektornykh polei”, Dokl. AN RUz., 2011, no. 5, 5–7
[10] Aslonov Zh. O. Narmanov A., “Geometriya orbit vektornykh polei Killinga”, Uzbek. mat. zh., 2012, no. 2, 77–85 | MR
[11] Berestovskii V. N., Nikonorov Yu. G., “Killingovy vektornye polya postoyannoi dliny na rimanovykh mnogoobraziyakh”, Sib. mat. zh., 49:3 (2008), 497–514 | MR | Zbl
[12] Kobayasi Sh., Nomidzu K., Osnovy differentsialnoi geometrii. T. 1, Nauka, M., 1981 | MR
[13] Narmanov A. Ya., “O differentsialnoi geometrii sloenii s osobennostyami”, Dokl. AN RUz., 1996, no. 3, 6–7 | Zbl
[14] Narmanov A. Ya., “O transversalnoi strukture mnozhestv upravlyaemosti simmetrichnykh sistem upravleniya”, Differ. uravn., 32:6 (1996), 780–783 | MR | Zbl
[15] Narmanov A. Ya., Struktura orbit sistem vektornykh polei i ikh predelnye svoistva, Diss. na soisk. uch. step. dokt. fiz.-mat. nauk, Tashkent, 1998
[16] Narmanov A. Ya., Saitova S. S., “O geometrii vektornykh polei Killinga”, Dokl. AN RUz., 2013, no. 5, 3–5
[17] Narmanov A. Ya., Saitova S. S., “O geometrii orbit vektornykh polei Killinga”, Differ. uravn., 50:12 (2014), 1582–1589 | Zbl
[18] Narmanov A. Ya., Aslonov J. O., On the geometry of the orbits of Killing vector fields, arXiv: 1203.3690 [math.DG] | MR
[19] Hermann R., “The differential geometry of foliations, I”, Ann. Math., 72 (1960), 445–457 | DOI | MR | Zbl
[20] Hermann R., “The differential geometry of foliations, II”, J. Math. Mech., 11 (1962), 305–315 | MR
[21] Molino P., “Orbit-like foliations”, Geometric Study of Foliations, World Scientific, Tokyo, 1993, 97–119 | MR
[22] Molino P., Riemannian Foliations, Birkhäuser, Boston, 1988 | MR | Zbl
[23] Morgan A., “Holonomy and metric properties of foliations in higher codimension”, Proc. Am. Math. Soc., 58 (1976), 255–261 | DOI | MR | Zbl
[24] Narmanov A. Ya., Qosimov O. Y., “On the geometry of the set of orbits of Killing vector fields on Euclidean space”, J. Geom. Symm. Phys., 55 (2020), 39–49 | DOI | MR | Zbl
[25] Reinhart B., “Foliated manifolds with bundle-like metrics”, Ann. Math., 69 (1959), 119–132 | DOI | MR | Zbl
[26] Stefan P., “Accessible sets, orbits and foliations with singularities”, Proc. London Math. Soc. $(3)$., 29 (1974), 699–713 | DOI | MR | Zbl
[27] Tamura I., Topology of Foliations: An Introduction, Am. Math. Soc., 2006 | MR
[28] Tondeur P., Foliations on Riemannian Manifolds, Springer-Verlag, New York, 1988 | MR | Zbl
[29] Tursunov B. A., “On the geometry of Riemannian submersions over orbit of Killing vector fields”, Bull. Math. Stat. Res., 4:2 (2016), 102–107 | MR