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

Yıl 2024, Cilt: 16 Sayı: 1, 184 - 198, 30.06.2024
https://doi.org/10.47000/tjmcs.1458966

Öz

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.

Teşekkür

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

Kaynakça

  • 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.
Yıl 2024, Cilt: 16 Sayı: 1, 184 - 198, 30.06.2024
https://doi.org/10.47000/tjmcs.1458966

Öz

Kaynakça

  • 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.
Toplam 26 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Cebirsel ve Diferansiyel Geometri
Bölüm Makaleler
Yazarlar

Abderrahım Zagane 0000-0001-9339-3787

Yayımlanma Tarihi 30 Haziran 2024
Gönderilme Tarihi 26 Mart 2024
Kabul Tarihi 10 Mayıs 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 16 Sayı: 1

Kaynak Göster

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. Haziran 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, sy. 1 (Haziran 2024): 184-98. https://doi.org/10.47000/tjmcs.1458966.
EndNote Zagane A (01 Haziran 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, c. 16, sy. 1, ss. 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 (Haziran 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, c. 16, sy. 1, 2024, ss. 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.