Let $(M_n,g)$ be a Riemannian manifold and $TM_n$ the total space of its tangent bundle. In this paper, we determine the infinitesimal fiber-preserving holomorphically projective (IFHP) transformations on $TM_n$ with respect to the Levi-Civita connection of the deformed complete lift metric $\tilde{G}_f=g^C+(fg)^V$, where $f$ is a nonzero differentiable function on $M_n$ and $g^C$ and $g^V$ are the complete lift and the vertical lift of $g$ on $TM_n$, respectively. Morevore, we prove that every IFHP transformation on $(TM_n,\tilde{G}_f)$ is reduced to an affine and induces an infinitesimal affine transformation on $(M_n,g)$.
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adapted almost complex structure. J. Hokkaido Univ. Educ. 53, 1-8 (2003).
[8] Hasegawa, I., Yamauchi, K.: Infinitesimal holomorphically projective transformations on the tangent bundles with complete lift connection.
Differential Geometry-Dynamical Systems. 7, 42-48 (2005).
[9] Hasegawa, I., Yamauchi, K.: On infinitesimal holomorphically projective transformations in compact Kaehlerian manifolds. Hokkaido Math. J. 8,
214-219 (1979).
[10] Ishihara, S.: Holomorphically projective changes and their groups in an almost complex manifold. Tohoku Math. J. 9, 273-297 (1957).
[11] Sasaki, S.: On the differential geometry of tangent bundles of Riemannian manifolds. Tohoku Math. J. 10, 338-358 (1958).
[12] Tachibana, S., Ishihara, S.: On infinitesimal holomorphically projective transformations in Kahlerian manifolds. Tohoku Math. J. 10, 77-101 (1960).
[13] Tarakci, O., Gezer, A., Salimov, A. A.: On solutions of IHPT equations on tangent bundle with the metric II+III. Math. Comput. Modelling. 50,
953-958 (2009).
[14] Yamauchi, K.: On infinitesimal conformal transformations of the tangent bundles over Riemannian manifolds. Ann. Rep. Asahikawa. Med. Coll.
16, 1-6 (1995).
[15] Yano, K.: The Theory of Lie Derivatives and Its Applications. Bibliotheca mathematica, North Holland Pub. Co. (1957).
[16] Yano, K., Ishihara, S.: Tangent and Cotangent Bundles. Marcel Dekker, Inc. New York (1973).
[17] Yano, K., Kobayashi, S.: Prolongation of tensor fields and connections to tangent bundles I, II, III. J. Math. Soc. Japan. 18, 194-210, 236–246 (1966),
19, 486-488 (1967).
[18] Zohrehvand, M.: IFHP transformations on the tangent bundle of a Riemannian manifold with a class of pseudo-Riemannian metrics. C. R. Acad.
Bulg. Sci. 73 (2), 170-178 (2020).
[19] Zohrehvand, M.: Projective vector fields on the tangent bundle with the deformed complete lift metrics. Balkan J. Geom. Appl. 25 (2), 170-178
(2020).
Year 2022,
Volume: 15 Issue: 1, 153 - 159, 30.04.2022
[1] Abbassi, M.T.K., Sarih, M.: On natural metrics on tangent bundles of Riemannian manifolds. Arch. Math. (Brno) Tomus. 41, 71-92 (2005).
[2] Abbassi, M.T.K., Sarih, M.: On Riemannian g-natural metrics of the form ags + bgh + cgv on the tangent bundle of a Riemannian manifold
(M; g). Mediterr. J. Math. 2, 19-43 (2005).
[4] Gezer, A.: On infinitesimal conformal transformations of the tangent bundles with the synectic lift of a Riemannian metric. Proc. Indian Acad. Sci.
(Math. Sci.) 119 (3), 345-350 (2009).
[5] Gezer, A.: On infinitesimal holomorphically projective transformations on the tangent bundles with respect to the Sasaki metric. Proceedings of the
Estonian Academy of Sciences. 60 (3), 149-157 (2011).
[6] Gezer, A., Özkan, M.: Notes on the tangent bundle with deformed complete lift metric. Turkish Journal of Mathematics. 38, 1038-1049 (2014).
[7] Hasegawa, I., Yamauchi, K.: Infinitesimal holomorphically projective transformations on the tangent bundles with horizontal lift connection and
adapted almost complex structure. J. Hokkaido Univ. Educ. 53, 1-8 (2003).
[8] Hasegawa, I., Yamauchi, K.: Infinitesimal holomorphically projective transformations on the tangent bundles with complete lift connection.
Differential Geometry-Dynamical Systems. 7, 42-48 (2005).
[9] Hasegawa, I., Yamauchi, K.: On infinitesimal holomorphically projective transformations in compact Kaehlerian manifolds. Hokkaido Math. J. 8,
214-219 (1979).
[10] Ishihara, S.: Holomorphically projective changes and their groups in an almost complex manifold. Tohoku Math. J. 9, 273-297 (1957).
[11] Sasaki, S.: On the differential geometry of tangent bundles of Riemannian manifolds. Tohoku Math. J. 10, 338-358 (1958).
[12] Tachibana, S., Ishihara, S.: On infinitesimal holomorphically projective transformations in Kahlerian manifolds. Tohoku Math. J. 10, 77-101 (1960).
[13] Tarakci, O., Gezer, A., Salimov, A. A.: On solutions of IHPT equations on tangent bundle with the metric II+III. Math. Comput. Modelling. 50,
953-958 (2009).
[14] Yamauchi, K.: On infinitesimal conformal transformations of the tangent bundles over Riemannian manifolds. Ann. Rep. Asahikawa. Med. Coll.
16, 1-6 (1995).
[15] Yano, K.: The Theory of Lie Derivatives and Its Applications. Bibliotheca mathematica, North Holland Pub. Co. (1957).
[16] Yano, K., Ishihara, S.: Tangent and Cotangent Bundles. Marcel Dekker, Inc. New York (1973).
[17] Yano, K., Kobayashi, S.: Prolongation of tensor fields and connections to tangent bundles I, II, III. J. Math. Soc. Japan. 18, 194-210, 236–246 (1966),
19, 486-488 (1967).
[18] Zohrehvand, M.: IFHP transformations on the tangent bundle of a Riemannian manifold with a class of pseudo-Riemannian metrics. C. R. Acad.
Bulg. Sci. 73 (2), 170-178 (2020).
[19] Zohrehvand, M.: Projective vector fields on the tangent bundle with the deformed complete lift metrics. Balkan J. Geom. Appl. 25 (2), 170-178
(2020).
Zohrehvand, M. (2022). IFHP Transformations on the Tangent Bundle with the Deformed Complete Lift Metric. International Electronic Journal of Geometry, 15(1), 153-159. https://doi.org/10.36890/iejg.1037651
AMA
Zohrehvand M. IFHP Transformations on the Tangent Bundle with the Deformed Complete Lift Metric. Int. Electron. J. Geom. April 2022;15(1):153-159. doi:10.36890/iejg.1037651
Chicago
Zohrehvand, Mosayeb. “IFHP Transformations on the Tangent Bundle With the Deformed Complete Lift Metric”. International Electronic Journal of Geometry 15, no. 1 (April 2022): 153-59. https://doi.org/10.36890/iejg.1037651.
EndNote
Zohrehvand M (April 1, 2022) IFHP Transformations on the Tangent Bundle with the Deformed Complete Lift Metric. International Electronic Journal of Geometry 15 1 153–159.
IEEE
M. Zohrehvand, “IFHP Transformations on the Tangent Bundle with the Deformed Complete Lift Metric”, Int. Electron. J. Geom., vol. 15, no. 1, pp. 153–159, 2022, doi: 10.36890/iejg.1037651.
ISNAD
Zohrehvand, Mosayeb. “IFHP Transformations on the Tangent Bundle With the Deformed Complete Lift Metric”. International Electronic Journal of Geometry 15/1 (April 2022), 153-159. https://doi.org/10.36890/iejg.1037651.
JAMA
Zohrehvand M. IFHP Transformations on the Tangent Bundle with the Deformed Complete Lift Metric. Int. Electron. J. Geom. 2022;15:153–159.
MLA
Zohrehvand, Mosayeb. “IFHP Transformations on the Tangent Bundle With the Deformed Complete Lift Metric”. International Electronic Journal of Geometry, vol. 15, no. 1, 2022, pp. 153-9, doi:10.36890/iejg.1037651.
Vancouver
Zohrehvand M. IFHP Transformations on the Tangent Bundle with the Deformed Complete Lift Metric. Int. Electron. J. Geom. 2022;15(1):153-9.