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Year 2021, Volume: 9 Issue: 3, 124 - 132, 30.09.2021
https://doi.org/10.36753/mathenot.710119

Abstract

References

  • [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
  • [13] Musso,E.,Tricerri,F.:RiemannianMetricsonTangentBundles.Ann.Mat.Pura.Appl.150,1-19(1988).https: //doi.org/10.1007/BF01761461
  • [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
  • [18] Sasaki,S.: OnthedifferentialgeometryoftangentbundlesofRiemannianmanifolds,II.TohokuMath.J.(2)14(2), 146-155 (1962). https://doi.org/10.2748/tmj/1178244169
  • [19] Sekizawa,M.: CurvaturesoftangentbundleswithCheeger-Gromollmetric.TokyoJ.Math.14(2),407-417(1991). DOI10.3836/tjm/1270130381
  • [20] Yano, K., Ishihara, S.: Tangent and tangent bundles. Marcel Dekker. INC. New York (1973).
  • [21] Zagane, A., Djaa, M.: On Geodesics of Warped Sasaki Metric. Mathematical Sciences and Applications E-Notes 5 (1), 85-92 (2017). https://doi.org/10.36753/mathenot.421709
  • [22] Zagane, A., Djaa, M.: Geometry of Mus-Sasaki metric. Commun. Math. 26 (2), 113-126 (2018). https://doi. org/10.2478/cm-2018-0008

Geodesics of Twisted-Sasaki Metric

Year 2021, Volume: 9 Issue: 3, 124 - 132, 30.09.2021
https://doi.org/10.36753/mathenot.710119

Abstract

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.

References

  • [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
  • [13] Musso,E.,Tricerri,F.:RiemannianMetricsonTangentBundles.Ann.Mat.Pura.Appl.150,1-19(1988).https: //doi.org/10.1007/BF01761461
  • [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
  • [18] Sasaki,S.: OnthedifferentialgeometryoftangentbundlesofRiemannianmanifolds,II.TohokuMath.J.(2)14(2), 146-155 (1962). https://doi.org/10.2748/tmj/1178244169
  • [19] Sekizawa,M.: CurvaturesoftangentbundleswithCheeger-Gromollmetric.TokyoJ.Math.14(2),407-417(1991). DOI10.3836/tjm/1270130381
  • [20] Yano, K., Ishihara, S.: Tangent and tangent bundles. Marcel Dekker. INC. New York (1973).
  • [21] Zagane, A., Djaa, M.: On Geodesics of Warped Sasaki Metric. Mathematical Sciences and Applications E-Notes 5 (1), 85-92 (2017). https://doi.org/10.36753/mathenot.421709
  • [22] Zagane, A., Djaa, M.: Geometry of Mus-Sasaki metric. Commun. Math. 26 (2), 113-126 (2018). https://doi. org/10.2478/cm-2018-0008
There are 22 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Zagane Abderrahım 0000-0001-9339-3787

Publication Date September 30, 2021
Submission Date March 27, 2020
Acceptance Date December 24, 2020
Published in Issue Year 2021 Volume: 9 Issue: 3

Cite

APA 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.

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