Класифiкацiя конформних векторних полiв на дотичному розшаруваннi
Анотація
Нехай $(M,g)$ — ріманів многовид, $TM$ — його дотичне розшарування з рімановою (або псевдорімановою) метрикою підняття, яка породжується $g.$ Наведено класифікацію нескінченно малих конформних перетворень, що зберігають шари на дотичному розшаруванні.
Посилання
Abbassi, Mohamed Tahar Kadaoui; Sarih, Maâti. Killing vector fields on tangent bundles with Cheeger–Gromoll metric. Tsukuba J. Math. 27 (2003), no. 2, 295–306. https://doi.org/10.21099/tkbjm/1496164650 DOI: https://doi.org/10.21099/tkbjm/1496164650
Bidabad, Behroz. Conformal vector fields on tangent bundle of Finsler manifolds. Balkan J. Geom. Appl. 11 (2006), no. 2, 28–35. https://www.emis.de/journals/BJGA/v11n2/B11-2-BI.pdf
Gezer, Aydin. On infinitesimal conformal transformations of the tangent bundles with the synectic lift of a Riemannian metric. Proc. Indian Acad. Sci. Math. Sci. 119 (2009), no. 3, 345–350. https://doi.org/10.1007/s12044-009-0033-0 DOI: https://doi.org/10.1007/s12044-009-0033-0
Gezer, Aydin; Bilen, Lokman. On infinitesimal conformal transformations with respect to the Cheeger–Gromoll metric. An. Ştiinţ. Univ. "Ovidius" Constanţa Ser. Mat. 20 (2012), no. 1, 113–127. https://doi.org/10.2478/v10309-012-0009-4 DOI: https://doi.org/10.2478/v10309-012-0009-4
Gezer, Aydin; Özkan, Mustafa. Notes on the tangent bundle with deformed complete lift metric. Turkish J. Math. 38 (2014), no. 6, 1038–1049. https://doi.org/10.3906/mat-1402-30 DOI: https://doi.org/10.3906/mat-1402-30
Hasegawa, Izumi; Yamauchi, Kazunari. Infinitesimal conformal transformations on tangent bundles with the lift metric I+II. Japanese Association of Mathematical Sciences 2001 Annual Meeting (Tennoji). Sci. Math. Jpn. 57 (2003), no. 1, 129–137. http://www.jams.or.jp/scm/contents/Vol-7-5/7-49.pdf
Peyghan, Esmaeil; Nasrabadi, Hassan; Tayebi, Akbar. The homogeneous lift to the (1,1)-tensor bundle of a Riemannian metric. Int. J. Geom. Methods Mod. Phys. 10 (2013), no. 4, 1350006, 18 pp. https://doi.org/10.1142/s0219887813500060 DOI: https://doi.org/10.1142/S0219887813500060
Peyghan, E.; Naderifard, A.; Tayebi, A. Almost paracontact structures on tangent sphere bundle. Int. J. Geom. Methods Mod. Phys 10 (2013), no. 9, 1320015, 11 pp. https://doi.org/10.1142/s0219887813200156 DOI: https://doi.org/10.1142/S0219887813200156
Peyghan, E.; Tayebi, A.; Nourmohammadifar, L. Cheeger–Gromoll type metrics on the (1,1)-tensor bundles.; translated from Izv. Nats. Akad. Nauk Armenii Mat. 48 (2013), no. 6, 59–70. J. Contemp. Math. Anal. 48 (2013), no. 6, 247–258 https://doi.org/10.3103/s1068362313060022 DOI: https://doi.org/10.3103/S1068362313060022
Peyghan, Esmaeil; Tayebi, Akbar; Zhong, ChunPing. Foliations on the tangent bundle of Finsler manifolds. Sci. China Math. 55 (2012), no. 3, 647–662. https://doi.org/10.1007/s11425-011-4288-4 DOI: https://doi.org/10.1007/s11425-011-4288-4
Peyghan, Esmaeil; Tayebi, Akbar; Zhong, Chunping. Horizontal Laplacian on tangent bundle of Finsler manifold with g-natural metric. Int. J. Geom. Methods Mod. Phys. 9 (2012), no. 7, 1250061, 18 pp. https://doi.org/10.1142/s0219887812500612 DOI: https://doi.org/10.1142/S0219887812500612
Peyghan, E.; Tayebi, A. Finslerian complex and Kählerian structures. Nonlinear Anal. Real World Appl. 11 (2010), no. 4, 3021–3030. https://doi.org/10.1016/j.nonrwa.2009.10.022 DOI: https://doi.org/10.1016/j.nonrwa.2009.10.022
Peyghan, Esmaeil; Tayebi, Akbar. On Finsler manifolds whose tangent bundle has the g-natural metric. Int. J. Geom. Methods Mod. Phys. 8 (2011), no. 7, 1593–1610. https://doi.org/10.1142/s0219887811005828 DOI: https://doi.org/10.1142/S0219887811005828
Peyghan, Esmaeil; Tayebi, Akbar. Killing vector fields of horizontal Liouville type. C. R. Math. Acad. Sci. Paris 349 (2011), no. 3-4, 205–208. https://doi.org/10.1016/j.crma.2011.01.009 DOI: https://doi.org/10.1016/j.crma.2011.01.009
Tayebi, Akbar; Peyghan, Esmaeil. On a class of Riemannian metrics arising from Finsler structures. C. R. Math. Acad. Sci. Paris 349 (2011), no. 5-6, 319–322. https://doi.org/10.1016/j.crma.2011.01.021 DOI: https://doi.org/10.1016/j.crma.2011.01.021
Salimov, Arif; Gezer, Aydin. On the geometry of the (1,1)-tensor bundle with Sasaki type metric. Chin. Ann. Math. Ser. B 32 (2011), no. 3, 369–386. https://doi.org/10.1007/s11401-011-0646-3 DOI: https://doi.org/10.1007/s11401-011-0646-3
Salimov, A. A.; Iscan, M.; Akbulut, K. Notes on para-Norden-Walker 4-manifolds. Int. J. Geom. Methods Mod. Phys. 7 (2010), no. 8, 1331–1347. https://doi.org/10.1142/s021988781000483x DOI: https://doi.org/10.1142/S021988781000483X
Salimov, A. A.; Akbulut, K.; Aslanci, S. A note on integrability of almost product Riemannian structures. Arab. J. Sci. Eng. Sect. A Sci. 34 (2009), no. 1, 153–157. https://www.researchgate.net/publication/266678391_A_note_on_integrability_of_almost_product_riemannian_structures
Tanno, Shûkichi. Killing vectors and geodesic flow vectors on tangent bundles. J. Reine Angew. Math. 282 (1976), 162–171. https://doi.org/10.1515/crll.1976.282.162 DOI: https://doi.org/10.1515/crll.1976.282.162
Yamauchi, K. On a infinitesimal conformal transformations of the tangent bundles with the metric I+III over Riemannian manifold, Ann. Rep. Asahikawa Med. Coll., 16 (1995), 1–6.
Yamauchi, K. On infinitesimal conformal transformations of the tangent bundles over Riemannian manifolds, Ann. Rep. Asahikawa Med. Coll., 15 (1994), 1–10 (1994).
Yano, Kentaro; Ishihara, Shigeru. Tangent and cotangent bundles: differential geometry. Pure and Applied Mathematics, No. 16. Marcel Dekker, Inc., New York, 1973. {rm ix}+423 pp. https://www.worldcat.org/title/tangent-and-cotangent-bundles-differential-geometry/oclc/713986
Для цієї роботи діють умови ліцензії Creative Commons Attribution 4.0 International License.
