On the Differential Geometry of Coframe Bundle with Cheeger-Gromoll Metric

Yıl 2022, Cilt: 15 Sayı: 2, 287 - 303, 31.10.2022

Habil Fattayev

https://doi.org/10.36890/iejg.1071782

Öz

In this paper we introduce the Cheeger-Gromoll type metric on the coframe bundle of a
Riemannian manifold and investigate the Levi-Civita connection, curvature tensor, sectional
curvature and geodesics of coframe bundle with this metric.

Anahtar Kelimeler

Coframe bundle, adapted frame, Cheeger-Gromoll metric, Levi-Civita connection, curvature tensor, geodesics.

Kaynakça

• [1] Agca, F., Salimov, A.: Some notes concerning Cheeger-Gromoll metrics. Hacet. J. Math. Stat. 42(5), (2013), 533-549.
• [2] Agca, F.: g−natural metrics on the cotangent bundle. IEJG, 6 (1), (2013), 129-146.
• [3] Cheeger, J., Gromoll, D.: On the structure of complete manifolds of nonnegative curvature. Ann. of Math. 96, (1972), 413-443.
• [4] Cordero, L., Dodson, C., Leon, M.: Differential geometry of frame bundles. Kluwer, Dordrecht, (1988).
• [5] Fattayev, H.,: Some notes on the differential geometry of linear coframe bundle of a Riemann manifold. Adv. Studies: Euro-Tbilisi Math. J. 14(4), (2021),81-95.
• [6] Gudmondson, S., Kappos, E.: On the geometry of the tangent bundles. Expo. Math. 20(1), (2002), 1-41.
• [7] Hou, Z., Sun, L.: Geometry of tangent bundle with Cheeger-Gromoll type metric. J. Math. Anal. Apll. 402, (2013), 493-504.
• [8] Kobayashi, S., Nomizu, K.: Foundations of differential Geometry, Vol. I. Interscience Publishers, New York-London, (1963).
• [9] Munteanu, M.: Cheeger-Gromoll type metrics on the tangent bundle. Sci. Ann. Univ. Agric. Sci. Vet. Med. 49(2), (2006), 257-268.
• [10] Musso, E., Tricerri, F .: Riemannian metrics on tangent bundles. Ann. Math. Pura. Appl. 150(4), (1988), 1-20.
• [11] Niedzialomski, K.: On the geometry of frame bundles. Archivum Mathematicum (BRNO). 48, (2012), 197-206.
• [12] Salimov, A., Akbulut, K.: A note on a paraholomorphic Cheeger-Gromoll metric. Proc. Indian Acad. Sci. 119(2), (2009), 187-195.
• [13] Salimov, A., Kazimova, S.: Geodesics of the Cheeger-Gromoll metric. Turk J Math. 33, (2009), 99-105.
• [14] Sekizawa, M.: Curvatures of tangent bundles with Cheeger-Gromoll metric. Tokyo J. Math. 14(2), (1991), 407-417.
• [15] Yano, K., Ishihara, S.: Tangent and cotangent bundles. Marsel Dekker Inc., New York, (1973).