[1] Abbassi, M. T. K., Sarih, M.: On Natural Metrics on Tangent Bundles of Riemannian Manifolds. Arch. Math. (Brno) 41, 71-92 (2005).
[2] Cengiz, N., Salimov, A. A.: Diagonal lift in the tensor bundle and its applications. Appl. Math. Comput. 142(2-3), 309-319 (2003).
[3] Cheeger, J., Gromoll, D.: On the structure of complete manifolds of nonnegative curvature. Ann. of Math. (2) 96, 413-443 (1972). https://doi.org/10.2307/1970819
[4] Djaa, M., Gancarzewicz, J.: The geometry of tangent bundles of order r. boletin Academia Galega de Ciencias 4, 147-165 (1985).
[5] Djaa, N. E. H., Boulal, A., Zagane, A.: Generalized Warped Product Manifolds And Biharmonic Maps. Acta Math. Univ. Comenian. (N.S.) 81 (2), 283-298 (2012).
[6] Dombrowski, P.: On the Geometry of the Tangent Bundle. J. Reine Angew. Math. 210, 73-88 (1962). https: //doi.org/10.1515/crll.1962.210.73
[7] Gezer, A.: On the Tangent Bundle With Deformed Sasaki Metric. Int. Electron. J. Geom. 6 (2), 19-31 (2013).
[8] Gudmundsson, S., Kappos, E.:On the Geometry of the Tangent Bundle with the Cheeger-Gromoll Metric. Tokyo J.
Math. 25 (1), 75-83 (2002).
[9] Jian, W., Yong, W.: On the Geometry of Tangent Bundles with the Rescaled Metric. arXiv:1104.5584v1 [math.DG] 29
Apr 2011.
[10] Kada Ben Otmane, R., Zagane, A., Djaa, M.: On generalized Cheeger-Gromoll metric and harmonicity. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 69 (1), 629-645 (2020). https://doi.org/10.31801/cfsuasmas. 487296
[11] Kowalski, O., Sekizawa, M.: On Riemannian Geometry Of Tangent Sphere Bundles With Arbitrary Constant Radius.
Arch. Math. (Brno) 44, 391-401 (2008).
[12] Latti, F., Djaa, M., Zagane, A.: Mus-Sasaki Metric and Harmonicity. Mathematical Sciences and Applications
E-Notes 6 (1) 29-36 (2018). https://doi.org/10.36753/mathenot.421753
[14] Salimov, A. A., Gezer, A., Akbulut, K.: Geodesics of Sasakian metrics on tensor bundles. Mediterr. J. Math. 6 (2), 135-147 (2009). https://doi.org/10.1007/s00009-009-0001-z
[15] Salimov, A. A, Gezer, A.: On the geometry of the (1, 1)-tensor bundle with Sasaki type metric. Chin. Ann. Math. Ser. B 32 (3), 369-386 (2011). https://doi.org/10.1007/s11401-011-0646-3
[16] Salimov, A. A., Agca, F.: Some Properties of Sasakian Metrics in Cotangent Bundles. Mediterr. J. Math. 8 (2), 243-255 (2011). https://doi.org/10.1007/s00009-010-0080-x
[17] Salimov, A. A., Kazimova, S.: Geodesics of the Cheeger-Gromoll Metric. Turkish J. Math. 33, 99-105 (2009). doi:10.3906/mat-0804-24
The main purpose of the paper is to investigate geodesics on the tangent bundle with respect to the twisted-Sasaki metric. We establish a necessary and sufficient conditions under which a curve be a geodesic respect. Afterward, we also construct some examples of geodesics.
[1] Abbassi, M. T. K., Sarih, M.: On Natural Metrics on Tangent Bundles of Riemannian Manifolds. Arch. Math. (Brno) 41, 71-92 (2005).
[2] Cengiz, N., Salimov, A. A.: Diagonal lift in the tensor bundle and its applications. Appl. Math. Comput. 142(2-3), 309-319 (2003).
[3] Cheeger, J., Gromoll, D.: On the structure of complete manifolds of nonnegative curvature. Ann. of Math. (2) 96, 413-443 (1972). https://doi.org/10.2307/1970819
[4] Djaa, M., Gancarzewicz, J.: The geometry of tangent bundles of order r. boletin Academia Galega de Ciencias 4, 147-165 (1985).
[5] Djaa, N. E. H., Boulal, A., Zagane, A.: Generalized Warped Product Manifolds And Biharmonic Maps. Acta Math. Univ. Comenian. (N.S.) 81 (2), 283-298 (2012).
[6] Dombrowski, P.: On the Geometry of the Tangent Bundle. J. Reine Angew. Math. 210, 73-88 (1962). https: //doi.org/10.1515/crll.1962.210.73
[7] Gezer, A.: On the Tangent Bundle With Deformed Sasaki Metric. Int. Electron. J. Geom. 6 (2), 19-31 (2013).
[8] Gudmundsson, S., Kappos, E.:On the Geometry of the Tangent Bundle with the Cheeger-Gromoll Metric. Tokyo J.
Math. 25 (1), 75-83 (2002).
[9] Jian, W., Yong, W.: On the Geometry of Tangent Bundles with the Rescaled Metric. arXiv:1104.5584v1 [math.DG] 29
Apr 2011.
[10] Kada Ben Otmane, R., Zagane, A., Djaa, M.: On generalized Cheeger-Gromoll metric and harmonicity. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 69 (1), 629-645 (2020). https://doi.org/10.31801/cfsuasmas. 487296
[11] Kowalski, O., Sekizawa, M.: On Riemannian Geometry Of Tangent Sphere Bundles With Arbitrary Constant Radius.
Arch. Math. (Brno) 44, 391-401 (2008).
[12] Latti, F., Djaa, M., Zagane, A.: Mus-Sasaki Metric and Harmonicity. Mathematical Sciences and Applications
E-Notes 6 (1) 29-36 (2018). https://doi.org/10.36753/mathenot.421753
[14] Salimov, A. A., Gezer, A., Akbulut, K.: Geodesics of Sasakian metrics on tensor bundles. Mediterr. J. Math. 6 (2), 135-147 (2009). https://doi.org/10.1007/s00009-009-0001-z
[15] Salimov, A. A, Gezer, A.: On the geometry of the (1, 1)-tensor bundle with Sasaki type metric. Chin. Ann. Math. Ser. B 32 (3), 369-386 (2011). https://doi.org/10.1007/s11401-011-0646-3
[16] Salimov, A. A., Agca, F.: Some Properties of Sasakian Metrics in Cotangent Bundles. Mediterr. J. Math. 8 (2), 243-255 (2011). https://doi.org/10.1007/s00009-010-0080-x
[17] Salimov, A. A., Kazimova, S.: Geodesics of the Cheeger-Gromoll Metric. Turkish J. Math. 33, 99-105 (2009). doi:10.3906/mat-0804-24
Abderrahım, Z. (2021). Geodesics of Twisted-Sasaki Metric. Mathematical Sciences and Applications E-Notes, 9(3), 124-132. https://doi.org/10.36753/mathenot.710119
AMA
Abderrahım Z. Geodesics of Twisted-Sasaki Metric. Math. Sci. Appl. E-Notes. September 2021;9(3):124-132. doi:10.36753/mathenot.710119
Chicago
Abderrahım, Zagane. “Geodesics of Twisted-Sasaki Metric”. Mathematical Sciences and Applications E-Notes 9, no. 3 (September 2021): 124-32. https://doi.org/10.36753/mathenot.710119.
EndNote
Abderrahım Z (September 1, 2021) Geodesics of Twisted-Sasaki Metric. Mathematical Sciences and Applications E-Notes 9 3 124–132.
IEEE
Z. Abderrahım, “Geodesics of Twisted-Sasaki Metric”, Math. Sci. Appl. E-Notes, vol. 9, no. 3, pp. 124–132, 2021, doi: 10.36753/mathenot.710119.
ISNAD
Abderrahım, Zagane. “Geodesics of Twisted-Sasaki Metric”. Mathematical Sciences and Applications E-Notes 9/3 (September 2021), 124-132. https://doi.org/10.36753/mathenot.710119.
JAMA
Abderrahım Z. Geodesics of Twisted-Sasaki Metric. Math. Sci. Appl. E-Notes. 2021;9:124–132.
MLA
Abderrahım, Zagane. “Geodesics of Twisted-Sasaki Metric”. Mathematical Sciences and Applications E-Notes, vol. 9, no. 3, 2021, pp. 124-32, doi:10.36753/mathenot.710119.
Vancouver
Abderrahım Z. Geodesics of Twisted-Sasaki Metric. Math. Sci. Appl. E-Notes. 2021;9(3):124-32.