SavedAdd your journal

Journals / Hacettepe Journal of Mathematics and Statistics / 2013 / Cilt: 42 - Sayı: 5

SOME NOTES CONCERNING CHEEGER-GROMOLL METRICS

A A SALİMOV
Filiz AGCA
Pages
533–549
Publication Date
2022-10-18
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The purpose of this paper is to introduce Cheeger-Gromoll type metricon the cotangent bundle of Riemannian manifold and investigate curvature properties and geodesics on the cotangent bundle with respectto the Cheeger-Gromoll metric.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The purpose of this paper is to introduce Cheeger-Gromoll type metricon the cotangent bundle of Riemannian manifold and investigate curvature properties and geodesics on the cotangent bundle with respectto the Cheeger-Gromoll metric.
📊
Key Findings & Data:The purpose of this paper is to introduce Cheeger-Gromoll type metricon the cotangent bundle of Riemannian manifold and investigate curvature properties and geodesics on the cotangent bundle with respectto the Cheeger-Gromoll metric.
💡
Conclusion & Impact:The purpose of this paper is to introduce Cheeger-Gromoll type metricon the cotangent bundle of Riemannian manifold and investigate curvature properties and geodesics on the cotangent bundle with respectto the Cheeger-Gromoll metric.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Cheeger-Gromoll metric · cotangent bundle · vertical and horizontal lift

Abstract

The purpose of this paper is to introduce Cheeger-Gromoll type metricon the cotangent bundle of Riemannian manifold and investigate curvature properties and geodesics on the cotangent bundle with respectto the Cheeger-Gromoll metric.

🔖

Cite This Article

SALİMOV, A. A., AGCA, F. (2022). SOME NOTES CONCERNING CHEEGER-GROMOLL METRICS. Hacettepe Journal of Mathematics and Statistics, Cilt: 42 - Sayı: 5, 533–549. https://ajindex.com/articles/530442

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (9)

  1. Abbassi M.T.K., Sarih M. On natural metrics on tangent bundles of Riemannian manifolds, Arch. Math. (Brno) 41 (1), 71-92, 2005.
  2. Abbassi M.T.K., Sarih M. On Riemannian g-natural metrics of the form ag s + bg h + cg v on the tangent bundle of a Riemannian manifold (M,g), Mediterr. J. Math. 2 (1), 19-43, 200 Abbassi M.T.K., Sarih M. On some hereditary properties of Riemannian g-natural metrics on tangent bundles of Riemannian manifolds, Differential Geom. Appl., 22(1), 19-47, 2005.
  3. Cheeger J., Gromoll D. On the structure of complete manifolds of nonnegative curvature, Ann. of Math. 96, 413-443, 1972.
  4. Gudmundsson S., Kappos E. On the geometry of the tangent bundle with the CheegerGromoll metric, Tokyo J. Math. 25 (1), 75-83, 2002.
  5. Kobayashi S., Nomizu K. Foundations of differential Geometry, Vol. I, Interscience Publishers, New York-London, 1963. Munteanu M. I. Cheeger Gromoll type metrics on the tangent bundle, Sci. Ann. Univ. Agric. Sci. Vet. Med. 49(2), 257-268, 2006. Munteanu M. I. Some aspects on the geometry of the tangent bundles and tangent sphere bundles of a Riemannian manifold Mediterr. J. Math. 5, 43-59, 2008.
  6. Musso F., Tricerri F. Riemannian metric on tangent bundles, Ann. Math. Pura. Appl. 150(4), 1-19, 1988.
  7. Salimov A.A., Gezer A., Iscan M. On para-Kahler-Norden structures on the tangent bundles, Ann. Polon. Math. 103(3), 247-261, 2012.
  8. Salimov A.A., Kazimova S. Geodesics of the Cheeger-Gromoll metric, Turk. J. Math. 32 1-8, 2008. Sekizawa M. Curvatures of tangent bundles with Cheeger-Gromoll metric, Tokyo J. Math. 14, 407-417, 1991. Tamm I.E. Collection of scientific works, Sobranie nauchnyh trudov (Russian), II, Nauka, Moscow, 1975.
  9. Yano K., Ishihara S. Tangent and cotangent bundles, Marcel Dekker Inc., N.Y., 1973.