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Year 2025, Volume: 17 Issue: 1, 264 - 274, 30.06.2025
https://doi.org/10.47000/tjmcs.1683350

Abstract

References

  • Bahadır, O., Uddin, S., Slant submanifolds of golden Riemannian manifolds, Int. J. Math. Extensions, 13(2018), 23–39.
  • Bejancu, A., Schouten-Van Kampen and Vr˘anceanu connections on foliated manifolds, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (NS), 52(2006), 37–60.
  • Bisht, L., On Hsu-structure manifold, Nijenhuis tensor, Int. J. Adv. Res. Technol., 2(2013), 87–96.
  • Bisht, L., Shanker, S., On recurrent Hsu-structure manifold, Int. J. Eng. Res. Appl. (Ijera), 2(2012), 1323–1328.
  • Bisht, L., Shanker, S., Nijenhius tensor on hyperbolic Hsu-structure manifold, Int. J. Innov. Res. Sci. Eng. Technol., 2(2013), 6214–6220.
  • Bisht, L., Shanker, S., Flat H-curvature tensors on Hsu-structure manifold, Int. J. Math. Arch., 6(2015), 174–180.
  • Blaga, A.M., Hret¸canu, C.E., Golden warped product Riemannian manifolds, Lib. Math. (New Ser.), 37(2018), 39–50.
  • Blaga, A.M., Nannicini, A., Foliations induced by metallic structures, N. Y. J. Math., 29(2019), 771–791.
  • Crasmareanu, M., Hret¸canu, C.E., Golden differential geometry, Chaos Solitons Fractals, 38(2008), 1229–1238.
  • De, U., Gezer, A., Karaman, C., Results concerning semi-symmetric metric F-connections on the Hsu-B manifolds, Commun. Korean Math. Soc., 38(2023), 837–846.
  • Erdoğan, F.E., Yıldırım, C., Semi-invariant submanifolds of golden Riemannian manifolds, Aip Conf. Proc., 1833(2017).
  • Erdoğan, F.E., Yıldırım, C., On a study of the totally umbilical semi-invariant submanifolds of golden Riemannian manifolds, Politek. Derg., 21(2018), 967–970.
  • Etayo, F., Santamar´ıa, R., Upadhyay, A., On the geometry of almost golden Riemannian manifolds, Mediterr. J. Math., 14(2017), 1–14.
  • Gezer, A., Cengiz, N., Salimov, A., On integrability of golden Riemannian structures, Turk. J. Math., 37(2013), 693–703.
  • Gök, M., Keleş, S., Kılıç, E., Schouten and Vr˘anceanu connections on golden manifolds, Int. Electron. J. Geom., 12(2019), 169–181.
  • Holm, M., New insights in brane and Kaluza-Klein theory through almost product structures, arXiv, (1998), arXiv:hep-th/9812168v1.
  • Hretcanu, C.E., Submanifolds in Riemannian manifold with golden structure, Workshop on Finsler Geometry and Its Applications, Hungary, 2007.
  • Hretcanu, C.E., Blaga, A.M., Warped product submanifolds in locally golden Riemannian manifolds with a slant factor, Mathematics, 9(2021), 2125.
  • Hretcanu, C.E., Crasmareanu, M., On some invariant submanifolds in a Riemannian manifold with golden structure, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (NS), 53(2007), 199–211.
  • Hretcanu, C.E., Crasmareanu, M., Applications of the golden ratio on Riemannian manifolds, Turk. J. Math., 33(2009), 179–191.
  • Hsu, C.J., On some structures which are similar to the quaternion structure, Tohoku Math. J. Second Ser., 12(1960), 403–428.
  • Hsu, C.J., Note on the integrability of a certain structure on differentiable manifold, Tohoku Math. J. Second Ser., 12(1960), 349–360.
  • Ianus, S., Some almost product structures on manifolds with linear connection, Kodai Math. Semin. Rep., 23(1971), 305–310.
  • Nivas, R., Verma, G., Semi symmetric non-metric connection on a manifold with generalised Hsu-structure, Nepali Math. Sci. Rep., 23(2004), 27–34.
  • Nivas, R., Verma, N.K., Certain submanifolds of Hsu-structure sanifolds, Int. J. Math. Sci. Appl., 1(2011), 41–46.
  • Özkan, M., Prolongations of golden structures to tangent bundles, Differ. Geom. Dyn. Syst., 16(2014), 227–238.
  • Özkan, M., Yılmaz, F., Prolongations of golden structures to tangent bundles of order r, Commun. Fac. Sci. Univ. Ank. Ser. Math. Stat., 65(2016), 35–48.
  • Poyraz, N.Ö, Yaşar, E., Lightlike hypersurfaces of a golden semi-Riemannian manifold, Mediterr. J. Math., 14(2017), 1–20.
  • Schouten, J.A., Van Kampen, E.R., Zur Einbettungs-und Kr”ummungstheorie nichtholonomer Gebilde, Math. Ann., 103(1930), 752–783.
  • Singh, K., On integrability conditions of a manifold admitting the general algebraic Hsu-structure, J. Rajasthan Acad. Phys. Sci., 5(2006), 377–382.
  • Şahin, B., Akyol, M.A., Golden maps between golden Riemannian manifolds and constancy of certain maps, Math. Commun., 19(2014), 333–342.
  • Şahin, F., Şahin, B., Erdoğan, F.E., Norden golden manifolds with constant sectional curvature and their submanifolds, Mathematics, 11(2023), 3301.
  • Vranceanu, G., Sur quelques points de la th’eorie des espaces non holonomes, Bul. Fac. St. Cernauti., 5(1931), 177–205.

Almost Hsu-Golden Structures on Manifolds

Year 2025, Volume: 17 Issue: 1, 264 - 274, 30.06.2025
https://doi.org/10.47000/tjmcs.1683350

Abstract

This study aims to define a new structure inspired by the Hsu and golden structures, termed the almost Hsu-golden structure. We investigate certain properties of this structure and define the almost Hsu-golden $B$-manifold. Finally, we also examine integrability and parallelism conditions and give some curvature relations for the almost Hsu-golden structure.

References

  • Bahadır, O., Uddin, S., Slant submanifolds of golden Riemannian manifolds, Int. J. Math. Extensions, 13(2018), 23–39.
  • Bejancu, A., Schouten-Van Kampen and Vr˘anceanu connections on foliated manifolds, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (NS), 52(2006), 37–60.
  • Bisht, L., On Hsu-structure manifold, Nijenhuis tensor, Int. J. Adv. Res. Technol., 2(2013), 87–96.
  • Bisht, L., Shanker, S., On recurrent Hsu-structure manifold, Int. J. Eng. Res. Appl. (Ijera), 2(2012), 1323–1328.
  • Bisht, L., Shanker, S., Nijenhius tensor on hyperbolic Hsu-structure manifold, Int. J. Innov. Res. Sci. Eng. Technol., 2(2013), 6214–6220.
  • Bisht, L., Shanker, S., Flat H-curvature tensors on Hsu-structure manifold, Int. J. Math. Arch., 6(2015), 174–180.
  • Blaga, A.M., Hret¸canu, C.E., Golden warped product Riemannian manifolds, Lib. Math. (New Ser.), 37(2018), 39–50.
  • Blaga, A.M., Nannicini, A., Foliations induced by metallic structures, N. Y. J. Math., 29(2019), 771–791.
  • Crasmareanu, M., Hret¸canu, C.E., Golden differential geometry, Chaos Solitons Fractals, 38(2008), 1229–1238.
  • De, U., Gezer, A., Karaman, C., Results concerning semi-symmetric metric F-connections on the Hsu-B manifolds, Commun. Korean Math. Soc., 38(2023), 837–846.
  • Erdoğan, F.E., Yıldırım, C., Semi-invariant submanifolds of golden Riemannian manifolds, Aip Conf. Proc., 1833(2017).
  • Erdoğan, F.E., Yıldırım, C., On a study of the totally umbilical semi-invariant submanifolds of golden Riemannian manifolds, Politek. Derg., 21(2018), 967–970.
  • Etayo, F., Santamar´ıa, R., Upadhyay, A., On the geometry of almost golden Riemannian manifolds, Mediterr. J. Math., 14(2017), 1–14.
  • Gezer, A., Cengiz, N., Salimov, A., On integrability of golden Riemannian structures, Turk. J. Math., 37(2013), 693–703.
  • Gök, M., Keleş, S., Kılıç, E., Schouten and Vr˘anceanu connections on golden manifolds, Int. Electron. J. Geom., 12(2019), 169–181.
  • Holm, M., New insights in brane and Kaluza-Klein theory through almost product structures, arXiv, (1998), arXiv:hep-th/9812168v1.
  • Hretcanu, C.E., Submanifolds in Riemannian manifold with golden structure, Workshop on Finsler Geometry and Its Applications, Hungary, 2007.
  • Hretcanu, C.E., Blaga, A.M., Warped product submanifolds in locally golden Riemannian manifolds with a slant factor, Mathematics, 9(2021), 2125.
  • Hretcanu, C.E., Crasmareanu, M., On some invariant submanifolds in a Riemannian manifold with golden structure, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (NS), 53(2007), 199–211.
  • Hretcanu, C.E., Crasmareanu, M., Applications of the golden ratio on Riemannian manifolds, Turk. J. Math., 33(2009), 179–191.
  • Hsu, C.J., On some structures which are similar to the quaternion structure, Tohoku Math. J. Second Ser., 12(1960), 403–428.
  • Hsu, C.J., Note on the integrability of a certain structure on differentiable manifold, Tohoku Math. J. Second Ser., 12(1960), 349–360.
  • Ianus, S., Some almost product structures on manifolds with linear connection, Kodai Math. Semin. Rep., 23(1971), 305–310.
  • Nivas, R., Verma, G., Semi symmetric non-metric connection on a manifold with generalised Hsu-structure, Nepali Math. Sci. Rep., 23(2004), 27–34.
  • Nivas, R., Verma, N.K., Certain submanifolds of Hsu-structure sanifolds, Int. J. Math. Sci. Appl., 1(2011), 41–46.
  • Özkan, M., Prolongations of golden structures to tangent bundles, Differ. Geom. Dyn. Syst., 16(2014), 227–238.
  • Özkan, M., Yılmaz, F., Prolongations of golden structures to tangent bundles of order r, Commun. Fac. Sci. Univ. Ank. Ser. Math. Stat., 65(2016), 35–48.
  • Poyraz, N.Ö, Yaşar, E., Lightlike hypersurfaces of a golden semi-Riemannian manifold, Mediterr. J. Math., 14(2017), 1–20.
  • Schouten, J.A., Van Kampen, E.R., Zur Einbettungs-und Kr”ummungstheorie nichtholonomer Gebilde, Math. Ann., 103(1930), 752–783.
  • Singh, K., On integrability conditions of a manifold admitting the general algebraic Hsu-structure, J. Rajasthan Acad. Phys. Sci., 5(2006), 377–382.
  • Şahin, B., Akyol, M.A., Golden maps between golden Riemannian manifolds and constancy of certain maps, Math. Commun., 19(2014), 333–342.
  • Şahin, F., Şahin, B., Erdoğan, F.E., Norden golden manifolds with constant sectional curvature and their submanifolds, Mathematics, 11(2023), 3301.
  • Vranceanu, G., Sur quelques points de la th’eorie des espaces non holonomes, Bul. Fac. St. Cernauti., 5(1931), 177–205.
There are 33 citations in total.

Details

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

Büşra Ay 0000-0002-6882-2778

Mustafa Özkan 0000-0002-5883-2294

Publication Date June 30, 2025
Submission Date April 24, 2025
Acceptance Date May 27, 2025
Published in Issue Year 2025 Volume: 17 Issue: 1

Cite

APA Ay, B., & Özkan, M. (2025). Almost Hsu-Golden Structures on Manifolds. Turkish Journal of Mathematics and Computer Science, 17(1), 264-274. https://doi.org/10.47000/tjmcs.1683350
AMA Ay B, Özkan M. Almost Hsu-Golden Structures on Manifolds. TJMCS. June 2025;17(1):264-274. doi:10.47000/tjmcs.1683350
Chicago Ay, Büşra, and Mustafa Özkan. “Almost Hsu-Golden Structures on Manifolds”. Turkish Journal of Mathematics and Computer Science 17, no. 1 (June 2025): 264-74. https://doi.org/10.47000/tjmcs.1683350.
EndNote Ay B, Özkan M (June 1, 2025) Almost Hsu-Golden Structures on Manifolds. Turkish Journal of Mathematics and Computer Science 17 1 264–274.
IEEE B. Ay and M. Özkan, “Almost Hsu-Golden Structures on Manifolds”, TJMCS, vol. 17, no. 1, pp. 264–274, 2025, doi: 10.47000/tjmcs.1683350.
ISNAD Ay, Büşra - Özkan, Mustafa. “Almost Hsu-Golden Structures on Manifolds”. Turkish Journal of Mathematics and Computer Science 17/1 (June2025), 264-274. https://doi.org/10.47000/tjmcs.1683350.
JAMA Ay B, Özkan M. Almost Hsu-Golden Structures on Manifolds. TJMCS. 2025;17:264–274.
MLA Ay, Büşra and Mustafa Özkan. “Almost Hsu-Golden Structures on Manifolds”. Turkish Journal of Mathematics and Computer Science, vol. 17, no. 1, 2025, pp. 264-7, doi:10.47000/tjmcs.1683350.
Vancouver Ay B, Özkan M. Almost Hsu-Golden Structures on Manifolds. TJMCS. 2025;17(1):264-7.