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A Study of Para-K\"{a}hler-Norden Structures on Cotangent Bundle with The New Class of Metrics

Year 2021, Volume: 13 Issue: 2, 338 - 347, 31.12.2021

Abstract

The main purpose of the present paper is to study almost para-complex-Norden properties concerning new class of metrics on the cotangent bundle.

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References

  • [1] Ağca, F., g-Natural metrics on the cotangent bundle, Int. Electron. J. Geom., 6(1)(2013), 129–146.
  • [2] Ağca, F., Salimov, A.A., Some notes concerning Cheeger-Gromoll metrics, Hacet. J. Math. Stat., 42(5)(2013), 533–549.
  • [3] Cruceanu, V., Une classe de structures g´eom´etriques sur le fibre cotangent, Tensor (N.S.), 53(1993), 196–201.
  • [4] Cruceanu, V., Fortuny P., Gadea, P.M., A survey on paracomplex geometry, Rocky Mountain J. Math., 26(1996), 83–115.
  • [5] De Leon, M., Rodrigues P.R., Methods of Di erential Geometry in Analytical Mechanics, North-Holland Mathematics Studies, 1989.
  • [6] 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.
  • [7] Gezer, A., On the tangent bundle with deformed Sasaki metric, Int. Electron. J. Geom., 6(2)(2013), 19–31.
  • [8] Gezer, A., Altunbas, M., Notes on the rescaled Sasaki type metric on the cotangent bundle, Acta Math. Sci. Ser. B (Engl. Ed.) 34(1)(2014), 162–174.
  • [9] Gezer, A., Altunbas, M., On the geometry of the rescaled Riemannian metric on tensor bundles of arbitrary type, Kodai Math. J. 38(1)(2015), 37–64.
  • [10] Gezer, A. Altunbas, M., On the rescaled Riemannian metric of Cheeger Gromoll type on the cotangent bundle, Hacet. J. Math. Stat., 45(2)(2016), 355–365.
  • [11] Manev, M., Mekerov, D., On Lie groups as quasi-K¨ahler manifolds with killing Norden metric, Adv. Geom., 8(3)(2008),343–352.
  • [12] Ocak, F., Kazimova, S., On a new metric in the cotangent bundle, Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci., 38(1)(2018), 128–138.
  • [13] Patterson, E.M., Walker, A.G., Riemannian extensions, Quart. J.Math. Oxford Ser. 2(3)(1952), 19–28.
  • [14] Salimov, A.A., Ağca, F., Some properties of Sasakian metrics in cotangent bundles, Mediterr. J. Math., 8(2)(2011), 243–255.
  • [15] Salimov, A.A., Gezer, A., Iscan, M.,On para-Kahler-Norden structures on the tangent bundles, Ann. Polon. Math., 103(3)(2012), 247–261.
  • [16] 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.
  • [17] Salimov, A.A., Iscan, M., Etayo F., Para-holomorphic B-manifold and its properties, Topology Appl., 154(4)(2007), 925–933.
  • [18] Sasaki, S., On the differential geometry of tangent bundles of Riemannian manifolds II, Tohoku Math. J. 14(1962), 146–155.
  • [19] Sekizawa, M., Natural transformations of affine connections on manifolds to metrics on cotangent bundles, In: Proceedings of 14th Winter School on Abstract Analysis (Srni, 1986), Rend. Circ. Mat. Palermo 14(1987) 129–142.
  • [20] Wang, J., Wang, Y., On the geometry of tangent bundles with the rescaled metric, arXiv:1104.5584v1.
  • [21] Yano, K., Ako, M., On certain operators associated with tensor field, Kodai Math. Sem. Rep., 20(1968), 414–436.
  • [22] Yano, K., Ishihara, S., Tangent and Cotangent Bundle, Marcel Dekker Inc., New York, 1973.
  • [23] Zagane, A., A new class of metrics on the cotangent bundle, Bull. Transilv. Univ. Brasov Ser. III, 13(62)(1)(2020), 285–302.
  • [24] Zayatuev, B.V., On Some Classes of Almost-Hermitian Structures on the Tangent Bundle, Webs and Quasigroups. T.S.U., 2002.
Year 2021, Volume: 13 Issue: 2, 338 - 347, 31.12.2021

Abstract

References

  • [1] Ağca, F., g-Natural metrics on the cotangent bundle, Int. Electron. J. Geom., 6(1)(2013), 129–146.
  • [2] Ağca, F., Salimov, A.A., Some notes concerning Cheeger-Gromoll metrics, Hacet. J. Math. Stat., 42(5)(2013), 533–549.
  • [3] Cruceanu, V., Une classe de structures g´eom´etriques sur le fibre cotangent, Tensor (N.S.), 53(1993), 196–201.
  • [4] Cruceanu, V., Fortuny P., Gadea, P.M., A survey on paracomplex geometry, Rocky Mountain J. Math., 26(1996), 83–115.
  • [5] De Leon, M., Rodrigues P.R., Methods of Di erential Geometry in Analytical Mechanics, North-Holland Mathematics Studies, 1989.
  • [6] 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.
  • [7] Gezer, A., On the tangent bundle with deformed Sasaki metric, Int. Electron. J. Geom., 6(2)(2013), 19–31.
  • [8] Gezer, A., Altunbas, M., Notes on the rescaled Sasaki type metric on the cotangent bundle, Acta Math. Sci. Ser. B (Engl. Ed.) 34(1)(2014), 162–174.
  • [9] Gezer, A., Altunbas, M., On the geometry of the rescaled Riemannian metric on tensor bundles of arbitrary type, Kodai Math. J. 38(1)(2015), 37–64.
  • [10] Gezer, A. Altunbas, M., On the rescaled Riemannian metric of Cheeger Gromoll type on the cotangent bundle, Hacet. J. Math. Stat., 45(2)(2016), 355–365.
  • [11] Manev, M., Mekerov, D., On Lie groups as quasi-K¨ahler manifolds with killing Norden metric, Adv. Geom., 8(3)(2008),343–352.
  • [12] Ocak, F., Kazimova, S., On a new metric in the cotangent bundle, Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci., 38(1)(2018), 128–138.
  • [13] Patterson, E.M., Walker, A.G., Riemannian extensions, Quart. J.Math. Oxford Ser. 2(3)(1952), 19–28.
  • [14] Salimov, A.A., Ağca, F., Some properties of Sasakian metrics in cotangent bundles, Mediterr. J. Math., 8(2)(2011), 243–255.
  • [15] Salimov, A.A., Gezer, A., Iscan, M.,On para-Kahler-Norden structures on the tangent bundles, Ann. Polon. Math., 103(3)(2012), 247–261.
  • [16] 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.
  • [17] Salimov, A.A., Iscan, M., Etayo F., Para-holomorphic B-manifold and its properties, Topology Appl., 154(4)(2007), 925–933.
  • [18] Sasaki, S., On the differential geometry of tangent bundles of Riemannian manifolds II, Tohoku Math. J. 14(1962), 146–155.
  • [19] Sekizawa, M., Natural transformations of affine connections on manifolds to metrics on cotangent bundles, In: Proceedings of 14th Winter School on Abstract Analysis (Srni, 1986), Rend. Circ. Mat. Palermo 14(1987) 129–142.
  • [20] Wang, J., Wang, Y., On the geometry of tangent bundles with the rescaled metric, arXiv:1104.5584v1.
  • [21] Yano, K., Ako, M., On certain operators associated with tensor field, Kodai Math. Sem. Rep., 20(1968), 414–436.
  • [22] Yano, K., Ishihara, S., Tangent and Cotangent Bundle, Marcel Dekker Inc., New York, 1973.
  • [23] Zagane, A., A new class of metrics on the cotangent bundle, Bull. Transilv. Univ. Brasov Ser. III, 13(62)(1)(2020), 285–302.
  • [24] Zayatuev, B.V., On Some Classes of Almost-Hermitian Structures on the Tangent Bundle, Webs and Quasigroups. T.S.U., 2002.
There are 24 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Abderrahım Zagane 0000-0001-9339-3787

Zagane Mohammed 0000-0003-2508-0265

Publication Date December 31, 2021
Published in Issue Year 2021 Volume: 13 Issue: 2

Cite

APA Zagane, A., & Mohammed, Z. (2021). A Study of Para-K\"{a}hler-Norden Structures on Cotangent Bundle with The New Class of Metrics. Turkish Journal of Mathematics and Computer Science, 13(2), 338-347. https://doi.org/10.47000/tjmcs.867188
AMA Zagane A, Mohammed Z. A Study of Para-K\"{a}hler-Norden Structures on Cotangent Bundle with The New Class of Metrics. TJMCS. December 2021;13(2):338-347. doi:10.47000/tjmcs.867188
Chicago Zagane, Abderrahım, and Zagane Mohammed. “A Study of Para-K\"{a}hler-Norden Structures on Cotangent Bundle With The New Class of Metrics”. Turkish Journal of Mathematics and Computer Science 13, no. 2 (December 2021): 338-47. https://doi.org/10.47000/tjmcs.867188.
EndNote Zagane A, Mohammed Z (December 1, 2021) A Study of Para-K\"{a}hler-Norden Structures on Cotangent Bundle with The New Class of Metrics. Turkish Journal of Mathematics and Computer Science 13 2 338–347.
IEEE A. Zagane and Z. Mohammed, “A Study of Para-K\"{a}hler-Norden Structures on Cotangent Bundle with The New Class of Metrics”, TJMCS, vol. 13, no. 2, pp. 338–347, 2021, doi: 10.47000/tjmcs.867188.
ISNAD Zagane, Abderrahım - Mohammed, Zagane. “A Study of Para-K\"{a}hler-Norden Structures on Cotangent Bundle With The New Class of Metrics”. Turkish Journal of Mathematics and Computer Science 13/2 (December 2021), 338-347. https://doi.org/10.47000/tjmcs.867188.
JAMA Zagane A, Mohammed Z. A Study of Para-K\"{a}hler-Norden Structures on Cotangent Bundle with The New Class of Metrics. TJMCS. 2021;13:338–347.
MLA Zagane, Abderrahım and Zagane Mohammed. “A Study of Para-K\"{a}hler-Norden Structures on Cotangent Bundle With The New Class of Metrics”. Turkish Journal of Mathematics and Computer Science, vol. 13, no. 2, 2021, pp. 338-47, doi:10.47000/tjmcs.867188.
Vancouver Zagane A, Mohammed Z. A Study of Para-K\"{a}hler-Norden Structures on Cotangent Bundle with The New Class of Metrics. TJMCS. 2021;13(2):338-47.