Abstract
UDC 514.7
Let
(
M
,
g
)
be a Riemannian manifold and
T
M
be its tangent bundle equipped with a Riemannian (or pseudo-Riemannian) lift metric derived from
g
.
We give a classification of infinitesimal fibre-preserving conformal transformations on the tangent bundle.
Publisher
Institute of Mathematics National Academy of Sciences of Ukraine
Reference22 articles.
1. 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
2. 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
3. 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
4. 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
5. 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