Some applications on tangent bundle with Kaluza-Klein metric

ISSN: 2147-5520
Başlangıç: 2015
Yayıncı: Biska Bilişim

In this paper, differential equations of geodesics; parallelism, incompressibility and closeness conditions of the horizontal and complete lift of the vector fields are investigated with respect to Kaluza-Klein metric on tangent bundle.

Keywords:

Kaluza-Klein metric tangent bundle, geodesics,

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Sasaki, S., On the differential geometry of tangent bundles of Riemannian manifolds, Tohoku Math. Journal, 10 (3), 338-354, 1958.
Dombrowski, P., On the differential geometry of tangent bundles, J. Reine Angew. Math., 210, 73–88, 1962.
Musso, E. and Tricerri F., Riemannian metrics on tangent bundles, Ann. Mat. Pura Appl. 150 (4), 1–19, 1988.
Sekizawa, M., Curvatures of tangent bundles with Cheeger–Gromoll metric, Tokyo J. Math. 14, 407–417, 1991.
Anastasiei, M., Locally conformal Kaehler structures on tangent bundle of a space form, Libertas Math. 19, 71–76, 1999.
Benyounes, M, Loubeau, E., and Todjihounde, L., Harmonic maps and Kaluza-Klein metrics on spheres, 42 (3), 791-821, 2012.
Mok, K.P., On the differential geometry of frame bundles of Riemannian manifolds, J.für die reine und angewandte Math., 302, 16-31, 1978.
Yano, K., and Ishihara S., Tangent and cotangent bundles, Marcel Dekker, 1973.
Salimov, A. and Kazimova S., Geodesics of the Cheeger-Gromoll metric, Turkish J. of Math., 33, 99-105, 2009.
Gezer, A. and Altunbaş, M., Some notes concerning Riemannian metrics of Cheeger-Gromoll type, J. Math. Anal. Appl., 396, 119-132, 2012.