Mus-Sasaki Metric and Complex Structures

Abstract

In this paper we study the geometry of some paracomplex structures on tangent fiber bundle $TM$ equipped with a Mus-Sasaki metrics.

Keywords

• almost product manifold
• almost paracomplex Norden manifold
• Mus-Sasaki metrics

References

1. [1] Abbassi, M. T. K., & Sarih, M. (2005). On natural metrics on tangent bundles of Riemannian manifolds. Archivum Mathematicum, 41(1), 71-92.
2. [2] Cengiz, N., & Salimov, A. A. (2003). Diagonal lift in the tensor bundle and its applications. Applied mathematics and computation, 142(2-3), 309-319.
3. [3] Cheeger, J., & Gromoll, D. (1972). On the structure of complete manifolds of nonnegative curvature. Annals of Mathematics, 413-443.
4. [4] Djaa, M. & Gancarzewicz, J. (1985). The geometry of tangent bundles of order r. Boletin Academia , Galega de Ciencias, 4, 147-165.
5. [5] Dombrowski, P. (1962). On the Geometry of the Tangent Bundle, Journal für die reine und angewandte Mathematik, 210, 73-88.
6. [6] Gezer, A. (2013). On the tangent bundle with deormed sasaki metric, International Electronic Journal of Geometry, 6(2), 19-31.
7. [7] Gudmundsson, S. & Kappos, E. (2002). On the Geometry of the Tangent Bundle with the Cheeger-Gromoll Metric. Tokyo Journal of Mathematics, 25(1), 75-83.
8. [8] Kobayashi, S. & Nomizu, K. (1963). Foundation of differential geometry. Interscience Publisher, New York-London.

9. [9] Salimov, A.A., Gezer, A. & Akbulut, K. (2009). Geodesics of Sasakian metrics on tensor bundles. Mediterranean Journal of Mathematics, 6(2), 135-147.
10. [10] Salimov, A. A. & Kazimova, S. (2009). Geodesics of the Cheeger-Gromoll Metric. Turkish Journal of Mathematics, 33(1), 99-105
11. [11] Salimov, A. A & Gezer, A. (2011). On the geometry of the (1, 1)-tensor bundle with Sasaki type metric. Chinese Annals of Mathematics, Series B, 32(3), 369.
12. [12] Salimov, A. A., & Agca, F. (2011). Some Properties of Sasakian Metrics in Cotangent Bundles. Mediterranean Journal of Mathematics, 8(2), 243-255.
13. [13] Sasaki, S. (1962). On the differential geometry of tangent bundles of Riemannian manifolds II. Tohoku Mathematical Journal, Second Series, 14(2), 146-155.
14. [14] Sekizawa, M. (1991). Curvatures of Tangent Bundles with Cheeger-Gromoll Metric. Tokyo Journal of Mathematics, 14(2), 407-417.
15. [15] Tachibana, S. (1960). Analytic tensor and its generalization. Tohoku Mathematical Journal, Second Series, 12(2), 208-221.
16. [16] Yano, K. & Ishihara, S. (1973). Tangent and cotangent bundles. Marcel dekker, Inc., New York.
17. [17] Zagane, A. & Djaa, M. (2017). On geodesics of warped Sasaki metric. Mathematical sciences and Applications E-Notes. 5, 85-92.
18. [18] Zagane, A. & Djaa, M. (2018). Geometry of Mus-Sasaki metric. Communication in Mathematics. 26(2), 113-126.