On infinitesimal conformal transformations with respect to the Cheeger-Gromoll metric
By:
Open Access
|May 2013References
- [1] M. T. K. Abbassi, Note on the classification theorems of g-natural metricson the tangent bundle of a Riemannian manifold (M, g), Comment. Math. Univ. Carolin., 45 (2004), no. 4, 591-596.
- [2] M. T. K. Abbassi, M. Sarih, On some hereditary properties of Riemanniang-natural metrics on tangent bundles of Riemannian manifolds, Differential Geom. Appl., 22 (2005), no. 1, 19-47.
- [3] M. T. K. Abbassi, M. Sarih, On natural metrics on tangent bundles of Riemannian manifolds, Arch. Math., 41 (2005), 71-92.
- [4] M. T. K. Abbassi, M. Sarih, Killing vector fields on tangent bundleswith Cheeger-Gromoll metric, Tsukuba J. Math., 27 (2003), 295-306.
- [5] M. Benyounes, E. Loubeau, C.M. Wood, The geometry of generalised Cheeger-Gromoll metrics. Tokyo J. Math., 32 (2009), no. 2, 287-312.
- [6] M. C. Calvo, G. R. Keilhauer, Tensor fields of type (0,2) on the tangent bundle of a Riemannian Manifold, Geom. Dedicata, 71 (1998), no.2, 209-219.
- [7] J. Cheeger, D. Gromoll, On the structure of complete manifolds of non negative curvature, Ann. of Math., 96 (1972), 413-443.
- [8] P. Dombrowski, On the geometry of the tangent bundles, J. reine and an gew. Math., 210 (1962), 73-88.
- [9] A. Gezer, On infinitesimal conformal transformations of the tangent bundles with the synectic lift of a Riemannian metric, Proc. Indian Acad. Sci. Math. Sci., 119 (2009), no. 3, 345-350.
- [10] S. Gudmundsson, E. Kappos, On the geometry of the tangent bundles, Expo. Math., 20 (2002), 1-41.
- [11] I. Hasegawa, K. Yamauchi, Infinitesimal conformal transformations on tangent bundles with the lift metric I+II, Sci. Math. Jpn., 57 (2003), no.1, 129-137.
- [12] I. Kolar, P. W. Michor, J. Slovak, Natural operations in differential geometry, Springer-Verlang, Berlin, 1993.
- [13] O. Kowalski, M. Sekizawa, Natural transformation of Riemannian metrics on manifolds to metrics on tangent bundles-a classification- , Bull. Tokyo Gakugei Univ., 40 (1988), no. 4, 1-29.
- [14] M. I. Munteanu, Some aspects on the geometry of the tangent bundles and tangent sphere bundles of a Riemannian manifold, Mediterr. J. Math., 5 (2008), no.1, 43-59.
- [15] E. Musso, F. Tricerri, Riemannian Metrics on Tangent Bundles, Ann. Mat. Pura. Appl., 150 (1988), no. 4, 1-19.
- [16] V. Oproiu, Some classes of general natural almost Hermitian structures on tangent bundles, . Rev. Roumaine Math. Pures Appl., 48 (2003), no. 5-6, 521-533.
- [17] V. Oproiu, A generalization of natural almost Hermitian structures ont he tangent bundles, . Math. J. Toyama Univ., 22 (1999), 1-14.
- [18] V. Oproiu, N. Papaghiuc, Some new geometric structures of natural lift type on the tangent bundle, Bull. Math. Soc. Sci. Math. Roumanie (N.S.), 52 (2009), no. 3, 333-346.
- [19] V. Oproiu, N. Papaghiuc, General natural Einstein Kähler structures on tangent bundles, Differential Geom. Appl., 27 (2009), no. 3, 384-392.
- [20] V. Oproiu, N. Papaghiuc, Classes of almost anti-Hermitian structures on the tangent bundle of a Riemannian manifold, An. Stiin. Univ. Al. I. Cuza Iasi. Mat. (N.S.), 50 (2004), no. 1, 175-190.
- [21] V. Oproiu, N. Papaghiuc, On the geometry of tangent bundle of a(pseudo-) Riemannian manifold, An. tiin. Univ. Al. I. Cuza Iai. Mat. (N.S.), 44 (1998), no. 1, 67-83.
- [22] N. Papaghiuc, Some locally symmetric anti-Hermitian structures on the tangent bundle, An. tiin?. Univ. Al. I. Cuza Iai. Mat. (N.S.), 52 (2006), no. 2, 277-287.
- [23] N. Papaghiuc, Some geometric structures on the tangent bundle of a Riemannian manifold, Demonstratio Math., 37 (2004), no. 1, 215-228.
- [24] N. Papaghiuc, A locally symmetric pseudo-Riemannian structure on the tangent bundle, Publ. Math. Debrecen, 59 (2001), no. 3-4, 303-315.
- [25] N. Papaghiuc, A Ricci flat pseudo-Riemannian metric on the tangent bundle of a Riemannian manifold, Colloq. Math., 87 (2001), no. 2, 227-233.
- [26] A. A. Salimov, S. Kazimova, Geodesics of the Cheeger-Gromoll metric, Turk. J. Math., 33 (2009), 99-105.
- [27] S. Sasaki, On the differential geometry of tangent bundles of Riemannian manifolds, Tohoku Math. J., 10 (1958), 338-358.
- [28] M. Sekizawa, Curvatures of tangent bundles with Cheeger-Gromollmetric, Tokyo J. Math., 14 (1991), 407-417.
- [29] S. Tanno, Killing vectors and geodesic flow vectors on tangent bundles, J. Reine Angew. Math., 282 (1976), 162-171.
- [30] K. Yamauchi, On infinitesimal conformal transformations of the tangent bundles with the metric I+III over Riemannian manifold, Ann Rep. Asahikawa. Med. Coll., 16 (1995), 1-6.
- [31] K. Yamauchi, On infinitesimal conformal transformations of the tangent bundles over Riemannian manifolds, Ann Rep. Asahikawa. Med. Coll., 15 (1994), 1-10.
- [32] K. Yano, On harmonic and Killing vector fields, Annals of Math., 55 (1952), 38-45.
- [33] K. Yano, S. Ishihara, Tangent and Cotangent Bundles, Marcel Dekker, Inc., New York 1973.
Language: English
Page range: 113 - 128
Published on: May 17, 2013
Published by: Ovidius University of Constanta
In partnership with: Paradigm Publishing Services
Publication frequency: 3 times per year
Keywords:
Related subjects:
© 2013 Aydin Gezer, Lokman Bilen, published by Ovidius University of Constanta
This work is licensed under the Creative Commons License.