CURVATURE PROPERTIES OF RIEMANNIAN METRICS OF THE FORM Sgf +H g ON THE TANGENT BUNDLE OVER A RIEMANNIAN MANIFOLD (M,g)

Year 2015, Volume: 8 Issue: 2, 181 - 194, 30.10.2015

Aydin Gezer , Lokman Bilen , Cağri Karaman Murat Altunbaş

https://doi.org/10.36890/iejg.592306

Cited By: 2

Abstract

Keywords

Metric connection , Riemannian metric , Riemannian curvature tensor , tangent bundle , Weyl curvature tensor

References

• [1] Abbassi, M. T. K.: Note on the classification theorems of g-natural metrics on the tangent bundle of a Riemannian manifold (M, g). Comment. Math. Univ. Carolin. 45, no. 4, 591- 596(2004).
• [2] 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 no. 1, 19-47 (2005).
• [3] Abbassi, M. T. K., Sarih, M.: On natural metrics on tangent bundles of Riemannian manifolds. Arch. Math., 41, 71-92 (2005).
• [4] Dombrowski, P.: On the geometry of the tangent bundles. J. reine and angew. Math. 210, 73-88 (1962).
• [5] Gezer, A., On the tangent bundle with deformed Sasaki metric. Int. Electron. J. Geom. 6, no. 2, 19–31, (2013).
• [6] Gezer, A., Altunbas, M.: Notes on the rescaled Sasaki type metric on the cotangent bundle, Acta Math. Sci. Ser. B Engl. Ed. 34 (2014), no. 1, 162–174.
• [7] Gezer, A., Tarakci, O., Salimov A. A.: On the geometry of tangent bundles with the metric II + III. Ann. Polon. Math. 97, no. 1, 73–85 (2010).
• [8] Hayden, H. A.:Sub-spaces of a space with torsion. Proc. London Math. Soc. S2-34, 27-50 (1932).
• [9] Kolar, I., Michor, P. W., Slovak, J.: Natural operations in differential geometry. Springer- Verlang, Berlin, 1993.
• [10] Kowalski, O.: Curvature of the Induced Riemannian Metric on the Tangent Bundle of a Riemannian Manifold. J. Reine Angew. Math. 250, 124-129 (1971).
• [11] Kowalski, O., Sekizawa, M.: Natural transformation of Riemannian metrics on manifolds to metrics on tangent bundles-a classification. Bull. Tokyo Gakugei Univ. 40 no. 4, 1-29 (1988).
• [12] Musso, E., Tricerri, F.: Riemannian Metrics on Tangent Bundles. Ann. Mat. Pura. Appl. 150, no. 4, 1-19 (1988).
• [13] Oproiu, V., Papaghiuc, N.: An anti-K¨ahlerian Einstein structure on the tangent bundle of a space form. Colloq. Math. 103, no. 1, 41–46 (2005).
• [14] Oproiu, V., Papaghiuc, N.: Einstein quasi-anti-Hermitian structures on the tangent bundle. An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.) 50, no. 2, 347–360 (2004).
• [15] Oproiu, V., Papaghiuc, N.: Classes of almost anti-Hermitian structures on the tangent bundle of a Riemannian manifold. An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.) 50, no. 1, 175–190 (2004).
• [16] Oproiu, V., Papaghiuc, N.: Some classes of almost anti-Hermitian structures on the tangent bundle. Mediterr. J. Math. 1 , no. 3, 269–282 (2004).
• [17] Sasaki, S.: On the differential geometry of tangent bundles of Riemannian manifolds. Tohoku Math. J. 10, 338-358 (1958).
• [18] Wang, J., Wang, Y.: On the geometry of tangent bundles with the rescaled metric.arXiv:1104.5584v1
• [19] Yano, K., Ishihara, S.: Tangent and Cotangent Bundles. Marcel Dekker, Inc., New York 1973.
• [20] Zayatuev, B. V.: On geometry of tangent Hermtian surface. Webs and Quasigroups. T.S.U. 139–143 (1995).
• [21] Zayatuev, B. V.: On some clases of AH-structures on tangent bundles. Proceedings of the International Conference dedicated to A. Z. Petrov [in Russian], pp. 53–54 (2000).
• [22] Zayatuev, B. V.: On some classes of almost-Hermitian structures on the tangent bundle. Webs and Quasigroups T.S.U. 103–106(2002).