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.
Keywords
Cheeger-Gromoll metric cotangent bundle vertical and horizontal lift curvature tensor geodesics
References
- Abbassi M.T.K., Sarih M. On natural metrics on tangent bundles of Riemannian manifolds, Arch. Math. (Brno) 41 (1), 71-92, 2005.
- 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. Cheeger J., Gromoll D. On the structure of complete manifolds of nonnegative curvature, Ann. of Math. 96, 413-443, 1972.
- Gudmundsson S., Kappos E. On the geometry of the tangent bundle with the CheegerGromoll metric, Tokyo J. Math. 25 (1), 75-83, 2002.
- 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.
- Musso F., Tricerri F. Riemannian metric on tangent bundles, Ann. Math. Pura. Appl. 150(4), 1-19, 1988.
- Salimov A.A., Gezer A., Iscan M. On para-Kahler-Norden structures on the tangent bundles, Ann. Polon. Math. 103(3), 247-261, 2012.
- 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.
- Yano K., Ishihara S. Tangent and cotangent bundles, Marcel Dekker Inc., N.Y., 1973.
Abstract
References
- Abbassi M.T.K., Sarih M. On natural metrics on tangent bundles of Riemannian manifolds, Arch. Math. (Brno) 41 (1), 71-92, 2005.
- 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. Cheeger J., Gromoll D. On the structure of complete manifolds of nonnegative curvature, Ann. of Math. 96, 413-443, 1972.
- Gudmundsson S., Kappos E. On the geometry of the tangent bundle with the CheegerGromoll metric, Tokyo J. Math. 25 (1), 75-83, 2002.
- 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.
- Musso F., Tricerri F. Riemannian metric on tangent bundles, Ann. Math. Pura. Appl. 150(4), 1-19, 1988.
- Salimov A.A., Gezer A., Iscan M. On para-Kahler-Norden structures on the tangent bundles, Ann. Polon. Math. 103(3), 247-261, 2012.
- 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.
- Yano K., Ishihara S. Tangent and cotangent bundles, Marcel Dekker Inc., N.Y., 1973.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Research Article |
| Authors | |
| Publication Date | May 1, 2013 |
| Published in Issue | Year 2013 Volume: 42 Issue: 5 |