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

Year 2022, , 287 - 303, 31.10.2022
https://doi.org/10.36890/iejg.1071782

Abstract

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.

References

  • [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).
Year 2022, , 287 - 303, 31.10.2022
https://doi.org/10.36890/iejg.1071782

Abstract

References

  • [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).
There are 15 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Habil Fattayev 0000-0003-0861-3904

Publication Date October 31, 2022
Acceptance Date February 26, 2022
Published in Issue Year 2022

Cite

APA Fattayev, H. (2022). On the Differential Geometry of Coframe Bundle with Cheeger-Gromoll Metric. International Electronic Journal of Geometry, 15(2), 287-303. https://doi.org/10.36890/iejg.1071782
AMA Fattayev H. On the Differential Geometry of Coframe Bundle with Cheeger-Gromoll Metric. Int. Electron. J. Geom. October 2022;15(2):287-303. doi:10.36890/iejg.1071782
Chicago Fattayev, Habil. “On the Differential Geometry of Coframe Bundle With Cheeger-Gromoll Metric”. International Electronic Journal of Geometry 15, no. 2 (October 2022): 287-303. https://doi.org/10.36890/iejg.1071782.
EndNote Fattayev H (October 1, 2022) On the Differential Geometry of Coframe Bundle with Cheeger-Gromoll Metric. International Electronic Journal of Geometry 15 2 287–303.
IEEE H. Fattayev, “On the Differential Geometry of Coframe Bundle with Cheeger-Gromoll Metric”, Int. Electron. J. Geom., vol. 15, no. 2, pp. 287–303, 2022, doi: 10.36890/iejg.1071782.
ISNAD Fattayev, Habil. “On the Differential Geometry of Coframe Bundle With Cheeger-Gromoll Metric”. International Electronic Journal of Geometry 15/2 (October 2022), 287-303. https://doi.org/10.36890/iejg.1071782.
JAMA Fattayev H. On the Differential Geometry of Coframe Bundle with Cheeger-Gromoll Metric. Int. Electron. J. Geom. 2022;15:287–303.
MLA Fattayev, Habil. “On the Differential Geometry of Coframe Bundle With Cheeger-Gromoll Metric”. International Electronic Journal of Geometry, vol. 15, no. 2, 2022, pp. 287-03, doi:10.36890/iejg.1071782.
Vancouver Fattayev H. On the Differential Geometry of Coframe Bundle with Cheeger-Gromoll Metric. Int. Electron. J. Geom. 2022;15(2):287-303.