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Some Almost $B$-Structures on the Tangent Bundle Equipped with a Vertical Rescaled Metric

Year 2024, , 184 - 198, 30.06.2024
https://doi.org/10.47000/tjmcs.1458966

Abstract

In the present paper, we study some almost paracomplex structures on the tangent bundle with vertical rescaled metric and search conditions for the tangent bundle to become $B$-manifold, quasi-$B$-manifold.

Thanks

Dear Editor-in-Chief, Thank you for accepting submit article our manuscript " Some almost $B$-structures on the tangent bundle equipped with a vertical rescaled metric". 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

  • Abbassi, M.T.K., Sarih, M., On natural metrics on tangent bundles of Riemannian manifolds, Arch. Math. 41(2005), 71–92 .
  • Alekseevsky, D.V., Medori, C., Tomassini, A., Para-K¨ahler Einstein metrics on homogeneous manifolds, C. R. Acad. Sci. Paris, Ser. I, 347(2009), 69–72.
  • Bilen, L., Gezer, A., Some results on Riemannian g-natural metrics generated by classical lifts on the tangent bundle, Eurasian Math. J., 8(4)(2017), 18–34.
  • Bilen, L., Turanli, S., Gezer, A., On Kahler-Norden-Codazzi golden structures on pseudo-Riemannian manifolds, Int. J. Geom. Methods Mod. Phys., 15(2018), 1–10.
  • Cruceanu, V., Gadea, P.M., Munoz Masque, J., Para-Hermitian and para-K¨ahler manifolds, Quaderni Inst. Mat. Univ. Messina, 1(1995), 1–72.
  • Cruceanu, V., Fortuny, P., Gadea, P.M., A survey on paracomplex geometry, Rocky Mountain J. Math. 26(1996), 83–115.
  • De Le´on, M., Rodrigues, P.R., Methods of Differential Geometry in Analytical Mechanics, North-Holland Mathematics Studies, 1989.
  • 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.
  • Ganchev, G.T., Borisov, A.V., Note on the almost complex manifolds with a Norden metric, C. R. Acad. Bulgarie Sci., 39(5)(1986), 31–34.
  • Gezer, A., Bilen, L., Karaman, C., Altunbas, M., Curvature properties of Riemannian metrics of the forms Sgf + Hg on the tangent bundle over a Riemannian manifold (M, g), Int. Elec. J. Geo., 8(2)(2015), 181–194.
  • Gezer, A., Ozkan, M., Notes on the tangent bundle with deformed complete lift metric, Turkish J. Math., 38(2014), 1038–1049.
  • Libermann, P., Sur les structures presque paracomplexes, C. R. Acad. Sci. Paris, 234(1952), 2517–2519.
  • Manev, M., Mekerov, D., On Lie groups as quasi-K¨ahler manifolds with Killing Norden metric, Adv. Geom., 8(3)(2008), 343–352.
  • Patterson, E.M., Riemann extensions which have K¨ahler metrics, Proc. Roy. Soc. Edinburgh Sect. A, 64(1954), 113–126.
  • Rashevskij, P.K., The scalar field in a stratified space, Trudy Sem. Vektor. Tenzor. Anal., 6(1948), 225–248.
  • Salimov, A.A., Agca, F., Some Properties of Sasakian Metrics in Cotangent Bundles, Mediterr. J. Math. 8(2)(2011), 243–255.
  • Salimov, A.A., Gezer, A., Iscan, M., On para-K¨ahler-Norden structures on the tangent bundles, Ann. Polon. Math., 103(3)(2012), 247–261.
  • Salimov, A.A., Iscan, M., Akbulut, K., Notes on para-Norden-Walker 4-manifolds, Int. J. Geom., Methods Mod. Phys. 7(8)(2010), 1331–1347.
  • Salimov, A.A., Iscan, M., Etayo, F., Para-holomorphic B-manifold and its properties, Topology Appl., 154(4)(2007), 925–933.
  • Yano, K., Ako, M., On certain operators associated with tensor field, Kodai Math. Sem. Rep., 20(1968), 414–436.
  • Yano, K., Ishihara, S., Tangent and Cotangent Bundles, Marcel Dekker, INC. New York, 1973.
  • Zagane, A., On para-K¨ahler-Norden properties of the φ-Sasaki metric on tangent bundle, Int. J. Maps Math., 4(2)(2021), 121–135.
  • Zagane, A., Para-complex Norden structures in cotangent bundle equipped with vertical rescaled Cheeger-Gromoll metric, J. Math. Phys. Anal. Geom., 17(3)(2021), 388–402.
  • 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., Zagane, M., A study of Para-K¨ahler-Norden structures on cotangent bundle with the new class of metrics, Turk. J. Math. Comput. Sci., 13(2)(2021), 338–347.
Year 2024, , 184 - 198, 30.06.2024
https://doi.org/10.47000/tjmcs.1458966

Abstract

References

  • Abbassi, M.T.K., Sarih, M., On natural metrics on tangent bundles of Riemannian manifolds, Arch. Math. 41(2005), 71–92 .
  • Alekseevsky, D.V., Medori, C., Tomassini, A., Para-K¨ahler Einstein metrics on homogeneous manifolds, C. R. Acad. Sci. Paris, Ser. I, 347(2009), 69–72.
  • Bilen, L., Gezer, A., Some results on Riemannian g-natural metrics generated by classical lifts on the tangent bundle, Eurasian Math. J., 8(4)(2017), 18–34.
  • Bilen, L., Turanli, S., Gezer, A., On Kahler-Norden-Codazzi golden structures on pseudo-Riemannian manifolds, Int. J. Geom. Methods Mod. Phys., 15(2018), 1–10.
  • Cruceanu, V., Gadea, P.M., Munoz Masque, J., Para-Hermitian and para-K¨ahler manifolds, Quaderni Inst. Mat. Univ. Messina, 1(1995), 1–72.
  • Cruceanu, V., Fortuny, P., Gadea, P.M., A survey on paracomplex geometry, Rocky Mountain J. Math. 26(1996), 83–115.
  • De Le´on, M., Rodrigues, P.R., Methods of Differential Geometry in Analytical Mechanics, North-Holland Mathematics Studies, 1989.
  • 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.
  • Ganchev, G.T., Borisov, A.V., Note on the almost complex manifolds with a Norden metric, C. R. Acad. Bulgarie Sci., 39(5)(1986), 31–34.
  • Gezer, A., Bilen, L., Karaman, C., Altunbas, M., Curvature properties of Riemannian metrics of the forms Sgf + Hg on the tangent bundle over a Riemannian manifold (M, g), Int. Elec. J. Geo., 8(2)(2015), 181–194.
  • Gezer, A., Ozkan, M., Notes on the tangent bundle with deformed complete lift metric, Turkish J. Math., 38(2014), 1038–1049.
  • Libermann, P., Sur les structures presque paracomplexes, C. R. Acad. Sci. Paris, 234(1952), 2517–2519.
  • Manev, M., Mekerov, D., On Lie groups as quasi-K¨ahler manifolds with Killing Norden metric, Adv. Geom., 8(3)(2008), 343–352.
  • Patterson, E.M., Riemann extensions which have K¨ahler metrics, Proc. Roy. Soc. Edinburgh Sect. A, 64(1954), 113–126.
  • Rashevskij, P.K., The scalar field in a stratified space, Trudy Sem. Vektor. Tenzor. Anal., 6(1948), 225–248.
  • Salimov, A.A., Agca, F., Some Properties of Sasakian Metrics in Cotangent Bundles, Mediterr. J. Math. 8(2)(2011), 243–255.
  • Salimov, A.A., Gezer, A., Iscan, M., On para-K¨ahler-Norden structures on the tangent bundles, Ann. Polon. Math., 103(3)(2012), 247–261.
  • Salimov, A.A., Iscan, M., Akbulut, K., Notes on para-Norden-Walker 4-manifolds, Int. J. Geom., Methods Mod. Phys. 7(8)(2010), 1331–1347.
  • Salimov, A.A., Iscan, M., Etayo, F., Para-holomorphic B-manifold and its properties, Topology Appl., 154(4)(2007), 925–933.
  • Yano, K., Ako, M., On certain operators associated with tensor field, Kodai Math. Sem. Rep., 20(1968), 414–436.
  • Yano, K., Ishihara, S., Tangent and Cotangent Bundles, Marcel Dekker, INC. New York, 1973.
  • Zagane, A., On para-K¨ahler-Norden properties of the φ-Sasaki metric on tangent bundle, Int. J. Maps Math., 4(2)(2021), 121–135.
  • Zagane, A., Para-complex Norden structures in cotangent bundle equipped with vertical rescaled Cheeger-Gromoll metric, J. Math. Phys. Anal. Geom., 17(3)(2021), 388–402.
  • 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., Zagane, M., A study of Para-K¨ahler-Norden structures on cotangent bundle with the new class of metrics, Turk. J. Math. Comput. Sci., 13(2)(2021), 338–347.
There are 26 citations in total.

Details

Primary Language English
Subjects Algebraic and Differential Geometry
Journal Section Articles
Authors

Abderrahım Zagane 0000-0001-9339-3787

Publication Date June 30, 2024
Submission Date March 26, 2024
Acceptance Date May 10, 2024
Published in Issue Year 2024

Cite

APA Zagane, A. (2024). Some Almost $B$-Structures on the Tangent Bundle Equipped with a Vertical Rescaled Metric. Turkish Journal of Mathematics and Computer Science, 16(1), 184-198. https://doi.org/10.47000/tjmcs.1458966
AMA Zagane A. Some Almost $B$-Structures on the Tangent Bundle Equipped with a Vertical Rescaled Metric. TJMCS. June 2024;16(1):184-198. doi:10.47000/tjmcs.1458966
Chicago Zagane, Abderrahım. “Some Almost $B$-Structures on the Tangent Bundle Equipped With a Vertical Rescaled Metric”. Turkish Journal of Mathematics and Computer Science 16, no. 1 (June 2024): 184-98. https://doi.org/10.47000/tjmcs.1458966.
EndNote Zagane A (June 1, 2024) Some Almost $B$-Structures on the Tangent Bundle Equipped with a Vertical Rescaled Metric. Turkish Journal of Mathematics and Computer Science 16 1 184–198.
IEEE A. Zagane, “Some Almost $B$-Structures on the Tangent Bundle Equipped with a Vertical Rescaled Metric”, TJMCS, vol. 16, no. 1, pp. 184–198, 2024, doi: 10.47000/tjmcs.1458966.
ISNAD Zagane, Abderrahım. “Some Almost $B$-Structures on the Tangent Bundle Equipped With a Vertical Rescaled Metric”. Turkish Journal of Mathematics and Computer Science 16/1 (June 2024), 184-198. https://doi.org/10.47000/tjmcs.1458966.
JAMA Zagane A. Some Almost $B$-Structures on the Tangent Bundle Equipped with a Vertical Rescaled Metric. TJMCS. 2024;16:184–198.
MLA Zagane, Abderrahım. “Some Almost $B$-Structures on the Tangent Bundle Equipped With a Vertical Rescaled Metric”. Turkish Journal of Mathematics and Computer Science, vol. 16, no. 1, 2024, pp. 184-98, doi:10.47000/tjmcs.1458966.
Vancouver Zagane A. Some Almost $B$-Structures on the Tangent Bundle Equipped with a Vertical Rescaled Metric. TJMCS. 2024;16(1):184-98.