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Some Notes on Geodesics of Vertical Rescaled Berger Deformation Metric in Tangent Bundle

Year 2022, Volume: 14 Issue: 1, 8 - 15, 30.06.2022
https://doi.org/10.47000/tjmcs.1079349

Abstract

In this paper, we study the geodesics on the tangent bundle $TM$ with respect to the vertical rescaled Berger deformation metric over an anti-paraK\"{a}hler manifold $(M, \varphi, g)$. In this case, we establish the necessary and sufficient conditions under which a curve be geodesic with respect to this. Finally, we also present certain examples of geodesic.

Thanks

Dear Editor-in-Chief, Thank you for accepting submit article our manuscript " Some notes on geodesics of vertical rescaled Berger deformation metric in tangent bundle". We would be very happy, if our manuscript meets the Journal of Publishing standards " Turkish Journal of Mathematics and Computer Science". Thanks again, Dr. Abderrahim ZAGANE

References

  • Altunbas, M., Simsek R., Gezer, A., A study concerning Berger type deformed Sasaki metric on the tangent bundle, Zh. Mat. Fiz. Anal.Geom., 15(4)(2019), 435-447.
  • Dida, H.M. Hathout, F., Azzouz, A., On the geometry of the tangent bundle with vertical rescaled metric, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68(1)(2019), 222-235.
  • Dombrowski, P., On the Geometry of the tangent bundle, J. Reine Angew. Math., 210(1962), 73-88.
  • Gudmundsson, S., Kappos, E., On the geometry of the tangent bundle with the Cheeger-Gromoll metric, Tokyo J. Math., 25(1)(2002), 75-83.
  • Musso, E., Tricerri, F., Riemannian metrics on tangent bundles, Ann. Mat. Pura. Appl., 150(1988), 1-19.
  • Salimov, A.A., Gezer, A., Akbulut, K., Geodesics of Sasakian metrics on tensor bundles, Mediterr. J. Math., 6(2)(2009), 135-147.
  • Salimov, A.A., Iscan, M., Etayo, F., Para-holomorphic $B$-manifold and its properties, Topology Appl., 154(4) (2007), 925-933.
  • Salimov A.A., Kazimova, S., Geodesics of the Cheeger-Gromoll metric, Turkish J. Math., 33(2009), 99-105.
  • Sasaki, S., On the differential geometry of tangent bundles of Riemannian manifolds II, Tohoku Math. J. (2), 14(2)(1962), 146-155.
  • Sekizawa, M., Curvatures of tangent bundles with Cheeger-Gromoll metric, Tokyo J. Math. , 14(2)(1991), 407-417.
  • Yampolsky, A., On geodesics of tangent bundle with fiberwise deformed Sasaki metric over Kahlerian manifolds, Zh. Mat. Fiz. Anal. Geom., 8(2)(2012), 177-189.
  • Yano, K., Ako, M., On certain operators associated with tensor fields, Kodai Math. Sem. Rep., 20(4)(1968), 414-436.
  • Yano, K., Ishihara, S., Tangent and Cotangent Bundle, Marcel Dekker Inc., New York, 1973.
  • Zagane, A., Djaa, M., On geodesics of warped Sasaki metric, Math. Sci. Appl. E-Notes, 5(1)(2017), 85-92.
  • Zagane, A., Berger type deformed Sasaki metric and harmonicity on the cotangent bundle, Int. Electron. J. Geom., 14(1)(2021), 183-195.
  • Zagane, A., Boussekkine, N., Some almost paracomplex structures on the tangent bundle with vertical rescaled Berger deformation metric, Balkan J. Geom. Appl., 26(1)(2021), 124-140.
  • Zagane, A., Berger type deformed Sasaki metric on the cotangent bundle, Commun. Korean Math. Soc., 36(3)(2021), 575-592.
  • Zagane, A., Some notes on Berger type deformed Sasaki metric in the cotangent bundle, Int. Electron. J. Geom., 14(2)(2021), 348-360.
  • Zagane, A., Vertical rescaled berger deformation metric on the tangent bundle, Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci., 41(4)(2021), 166-180.
  • Zagane, A., A study of harmonic sections of tangent bundles with vertically rescaled Berger-type deformed Sasaki metric, Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerb., 47(2)(2021), 270-285.
Year 2022, Volume: 14 Issue: 1, 8 - 15, 30.06.2022
https://doi.org/10.47000/tjmcs.1079349

Abstract

References

  • Altunbas, M., Simsek R., Gezer, A., A study concerning Berger type deformed Sasaki metric on the tangent bundle, Zh. Mat. Fiz. Anal.Geom., 15(4)(2019), 435-447.
  • Dida, H.M. Hathout, F., Azzouz, A., On the geometry of the tangent bundle with vertical rescaled metric, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68(1)(2019), 222-235.
  • Dombrowski, P., On the Geometry of the tangent bundle, J. Reine Angew. Math., 210(1962), 73-88.
  • Gudmundsson, S., Kappos, E., On the geometry of the tangent bundle with the Cheeger-Gromoll metric, Tokyo J. Math., 25(1)(2002), 75-83.
  • Musso, E., Tricerri, F., Riemannian metrics on tangent bundles, Ann. Mat. Pura. Appl., 150(1988), 1-19.
  • Salimov, A.A., Gezer, A., Akbulut, K., Geodesics of Sasakian metrics on tensor bundles, Mediterr. J. Math., 6(2)(2009), 135-147.
  • Salimov, A.A., Iscan, M., Etayo, F., Para-holomorphic $B$-manifold and its properties, Topology Appl., 154(4) (2007), 925-933.
  • Salimov A.A., Kazimova, S., Geodesics of the Cheeger-Gromoll metric, Turkish J. Math., 33(2009), 99-105.
  • Sasaki, S., On the differential geometry of tangent bundles of Riemannian manifolds II, Tohoku Math. J. (2), 14(2)(1962), 146-155.
  • Sekizawa, M., Curvatures of tangent bundles with Cheeger-Gromoll metric, Tokyo J. Math. , 14(2)(1991), 407-417.
  • Yampolsky, A., On geodesics of tangent bundle with fiberwise deformed Sasaki metric over Kahlerian manifolds, Zh. Mat. Fiz. Anal. Geom., 8(2)(2012), 177-189.
  • Yano, K., Ako, M., On certain operators associated with tensor fields, Kodai Math. Sem. Rep., 20(4)(1968), 414-436.
  • Yano, K., Ishihara, S., Tangent and Cotangent Bundle, Marcel Dekker Inc., New York, 1973.
  • Zagane, A., Djaa, M., On geodesics of warped Sasaki metric, Math. Sci. Appl. E-Notes, 5(1)(2017), 85-92.
  • Zagane, A., Berger type deformed Sasaki metric and harmonicity on the cotangent bundle, Int. Electron. J. Geom., 14(1)(2021), 183-195.
  • Zagane, A., Boussekkine, N., Some almost paracomplex structures on the tangent bundle with vertical rescaled Berger deformation metric, Balkan J. Geom. Appl., 26(1)(2021), 124-140.
  • Zagane, A., Berger type deformed Sasaki metric on the cotangent bundle, Commun. Korean Math. Soc., 36(3)(2021), 575-592.
  • Zagane, A., Some notes on Berger type deformed Sasaki metric in the cotangent bundle, Int. Electron. J. Geom., 14(2)(2021), 348-360.
  • Zagane, A., Vertical rescaled berger deformation metric on the tangent bundle, Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci., 41(4)(2021), 166-180.
  • Zagane, A., A study of harmonic sections of tangent bundles with vertically rescaled Berger-type deformed Sasaki metric, Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerb., 47(2)(2021), 270-285.
There are 20 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Abderrahım Zagane 0000-0001-9339-3787

Publication Date June 30, 2022
Published in Issue Year 2022 Volume: 14 Issue: 1

Cite

APA Zagane, A. (2022). Some Notes on Geodesics of Vertical Rescaled Berger Deformation Metric in Tangent Bundle. Turkish Journal of Mathematics and Computer Science, 14(1), 8-15. https://doi.org/10.47000/tjmcs.1079349
AMA Zagane A. Some Notes on Geodesics of Vertical Rescaled Berger Deformation Metric in Tangent Bundle. TJMCS. June 2022;14(1):8-15. doi:10.47000/tjmcs.1079349
Chicago Zagane, Abderrahım. “Some Notes on Geodesics of Vertical Rescaled Berger Deformation Metric in Tangent Bundle”. Turkish Journal of Mathematics and Computer Science 14, no. 1 (June 2022): 8-15. https://doi.org/10.47000/tjmcs.1079349.
EndNote Zagane A (June 1, 2022) Some Notes on Geodesics of Vertical Rescaled Berger Deformation Metric in Tangent Bundle. Turkish Journal of Mathematics and Computer Science 14 1 8–15.
IEEE A. Zagane, “Some Notes on Geodesics of Vertical Rescaled Berger Deformation Metric in Tangent Bundle”, TJMCS, vol. 14, no. 1, pp. 8–15, 2022, doi: 10.47000/tjmcs.1079349.
ISNAD Zagane, Abderrahım. “Some Notes on Geodesics of Vertical Rescaled Berger Deformation Metric in Tangent Bundle”. Turkish Journal of Mathematics and Computer Science 14/1 (June 2022), 8-15. https://doi.org/10.47000/tjmcs.1079349.
JAMA Zagane A. Some Notes on Geodesics of Vertical Rescaled Berger Deformation Metric in Tangent Bundle. TJMCS. 2022;14:8–15.
MLA Zagane, Abderrahım. “Some Notes on Geodesics of Vertical Rescaled Berger Deformation Metric in Tangent Bundle”. Turkish Journal of Mathematics and Computer Science, vol. 14, no. 1, 2022, pp. 8-15, doi:10.47000/tjmcs.1079349.
Vancouver Zagane A. Some Notes on Geodesics of Vertical Rescaled Berger Deformation Metric in Tangent Bundle. TJMCS. 2022;14(1):8-15.