Geodesic
On Geometry of Foliations of Codimension $1$
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference «Problems of Modern Topology and its Applications», Tome 144 (2018), pp. 109-116 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, geometry and topology of foliations generated by level surfaces of metric functions are discussed. 
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     title = {On {Geometry} of {Foliations} of {Codimension~}$1$},
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A. M. Bayturaev. On Geometry of Foliations of Codimension $1$. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference «Problems of Modern Topology and its Applications», Tome 144 (2018), pp. 109-116. http://geodesic.mathdoc.fr/item/INTO_2018_144_a12/

[1] Bakelman I. Ya., Verner A. A., Kantor B. E., Vvedenie v differentsialnuyu geometriyu «v tselom», Nauka, M., 1973 | MR

[2] Bibikov Yu. N., Obyknovennye differentsialnye uravneniya, LGU, L., 1981

[3] Gromol D., Klingenberg V., Meier V., Rimanova geometriya v tselom, Mir, M., 1971

[4] Kaipnazarova G., Narmanov A. Ya., “Topologiya sloenii, porozhdennykh poverkhnostyami urovnya”, Uzbek. mat. zh., 2008, no. 2, 53–60 | MR | Zbl

[5] Kaipnazarova G. Kh., Geometriya sloenii, porozhdennykh poverkhnostyami urovnya, Diss. na soisk. uch. step. kand. fiz.-mat. nauk, In-t mat. inform. tekhn. AN RUz, Tashkent, 2009

[6] Kobayasi Sh., Nomidzu K., Osnovy differentsialnoi geometrii, v. 1, Nauka, M., 1981 | MR

[7] Kobayasi Sh., Nomidzu K., Osnovy differentsialnoi geometrii, v. 2, Nauka, M., 1981 | MR

[8] Narmanov A., Sharapov S., “O poverkhnostyakh urovnya submersii”, Uzbek. mat. zh., 2004, no. 2, 62–66 | MR

[9] Narmanov A., Kaipnazarova G., “Metricheskie funktsii na rimanovykh mnogoobraziyakh”, Uzbek. mat. zh., 2010, no. 1, 11–20

[10] Palis Zh., Di Melu, Geometricheskaya teoriya dinamicheskikh sistem, Mir, M., 1986

[11] Blumenthal R., Hebda J., “Complementary distributions which preserve the leaf geometry and applications to totally geodesic foliations”, Quart. J. Math., 35 (1984), 383–392 | DOI | MR | Zbl

[12] Molino P., Riemannian foliations, Progr. Math., 73, Birkhäuser Boston Inc., 1988 | MR | Zbl

[13] Tondeur P., Foliations on Riemannian manifolds, Springer-Verlag, 1988 | MR | Zbl