Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2023, Cilt: 15 Sayı: 2, 355 - 364, 31.12.2023
https://doi.org/10.47000/tjmcs.1355887

Öz

Kaynakça

  • Altunbas, M., Bilen, L.,Gezer, A., Remarks about the Kaluza-Klein metric on tangent bundle, Int. J. Geo. Met. Mod. Phys., 16(3)(2019), 1950040.
  • Azami, S., General natural metallic structure on tangent bundle, Iran J Sci Technol Trans Sci, 42(2018), 81—88.
  • Ali, S., Nivas, R., On submanifolds immersed in a manifold with quarter symmetric connection, Riv. Mat. Univ. Parma., 6(3)(2000), 11–23.
  • Bahadir, O., Lorentzian para-Sasakian manifold with quarter-symmetric non-metric connection, Journal of Dynamical Systems and Geometric Theories, 14(1)(2016), 17–33.
  • Bilen, L., Turanli, S., Gezer, A., On K¨ahler–Norden–Codazzi golden structures on pseudo-Riemannian manifolds, International Journal of Geometric Methods in Modern Physics, 15(2018), 1–10.
  • Chaubey, S.K., De, U.C., Characterization of the Lorentzian para-Sasakian manifolds admitting a quarter-symmetric non-metric connection, SUT Journal of Mathematics, 55(1)(2019), 53–67.
  • Choudhary, M.A., Khan, M.N.I., Siddiqi, M.D., Some basic inequalities on (ϵ)-Para Sasakian manifold, Symmetry, 14(12)(2022), 2585.
  • Das, L.S., Second order parallel tensors on para r-Sasakian manifolds with coefficient α, Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis, 28(2012), 83–88.
  • Das, L.S., Second order parallel tensor on α- Sasakian manifold, Acta Mathematica, Academiae Pedagogicae Nyiregyhaziensis, 23(1)(2007), 65–69.
  • Das, L.S., Khan, M.N.I., Symmetric and Ricci LP-Sasakian manifold, Mathematical Sciences Research Journal, 17(10)(2013), 263–268.
  • Das, L.S., Nivas, R., Khan, M.N.I., On Semi-invariant submanifolds of conformal K(ξ) contact Riemannian manifold, Algebras, Groups and Geometries, 23(1)(2006), 292–302.
  • De, U.C., Kamilya, D., Hypersurfaces of Rieamnnian manifold with semi-symmetric non-metric connection, J. Indian Inst. Sci., 75(1995), 707–710.
  • De, U.C., Mondal, A.K., Hypersurfaces of Kenmotsu manifolds endowed with a quarter-symmetric non-metric connection, Kuwait J. Sci. Eng., 39(2012), 43–56.
  • De, U.C., Mandal, D., Mandal, K., Some characterizations of Kenmotsu manifolds admitting a quarter-symmetric metric connection, Bull.Transilv. Univ. Bra¸sov Ser. III, 9(58)(1)(2016), 39–52.
  • Dida, H.M., Hathout, F., Ricci soliton on the tangent bundle with semi-symmetric metric connection, Bulletin of the Transilvania University of Brasov Series III: Mathematics and Computer Science, 1(63)(2)(2021), 37–52.
  • Dida, H.M., Ikemakhen, A., A class of metrics on tangent bundles of pseudo-Riemannian manifolds, Archivum Mathematicum (BRNO) Tomus, 47(2011), 293—308.
  • Dida, H.M., Hathout, F., Djaa, M., On the geometry of the second order tangent bundle with the diagonal lift metric, Int. Journal of Math. Analysis, 3(9)(2009), 443–456.
  • Friedmann, A., Schouten, J.A. , A¨Uber die geometrie der halbsymmetrischen A¨ubertragung, Math. Zeitschr., 21(1924), 211–223.
  • Golab, S., On semi-symmetric and quarter-symmetric linear connections, Tensor, N. S., 29(1975), 249–254.
  • Hayden, H.A., Subspaces of a space with torsion, Proc. London Math. Soc., 34(1932), 27–50.
  • Han, Y., Yun, H.T., Zhao, P., Some invariants of quarter-symmetric metric connections under the projective transformation, Filomat, 27(4)(2013), 679–691.
  • Kazan, A., Karadag, H.B., Locally decomposable golden tangent bundles with CheegerGromoll metric, Miskolc Math. Not., 17(1)(2016), 399–411.
  • Khan, M.N.I., Proposed theorems for lifts of the extended almost complex structures on the complex manifold, Asian-European Journal of Mathematics, 15(11)(2022), 2250200.
  • Khan, M.N.I., Novel theorems for the frame bundle endowed with metallic structures on an almost contact metric manifold, Chaos, Solitons & Fractals, 146(2021), 110872.
  • Khan, M.N.I., De, U.C., Liftings of metallic structures to tangent bundles of order r, AIMS Mathematics, 7(5)(2022), 7888–7897.
  • Khan, M.N.I., Das, L.S., On CR-structure and the general quadratic structure, Journal for Geometry and Graphics, 24(2)(2020), 249–255.
  • Khan, M.N.I., Jun, J.B., Covariant derivative of certain structures in tangent bundle, Journal of the Chungcheong Mathematical Society, 30(4)(2017), 387–396.
  • Khan, M.N.I., Choudhary, M.A., Chaubey, S.K., Alternative Equations for Horizontal Lifts of the Metallic Structures from Manifold onto Tangent Bundle, Journal of Mathematics, 2022(Article ID 5037620)(2022).
  • Khan, M.N.I., Submanifolds of a Riemannian manifold endowed with a new type of semi-symmetric non-metric connection in the tangent bundle, International Journal of Mathematics and Computer Science, 17(1)(2022), 265-–275.
  • Khan, M.N.I., Mofarreh, F., Haseeb, A., Tangent bundles of P-Sasakian manifolds endowed with a quarter-symmetric metric connection, Symmetry, 15(3)(2023), 753.
  • Khan, M.N.I., A note on certain structures in the tangent bundle, Far East Journal of Mathematical Sciences, 101(9)(2017), 1947–1965.
  • Khan, M.N.I., Mofarreh, F., Haseeb, A., Saxena, M., Certain results on the lifts from an LP-Sasakian manifold to its tangent bundle associated with a quarter-symmetric metric connection, Symmetry, 15(8)(2023), 1553.
  • Khan, M.N.I., De, U.C., Lifts of metallic structure on a cross section, Filomat, 36(18)(2023), 6369–6363.
  • Khan, M.N.I., Liftings from a Para-Sasakian manifold to its tangent bundles, Filomat, 37(20)(2023), 6727–6740.
  • Khan, M.N.I., Novel theorems for metallic structures on the frame bundle of the second order, Filomat, 36(13)(2022), 4471–4482.
  • Khan, M.N.I., De, U.C., Velimirovic, L.S., Lifts of a quarter-symmetric metric connection from a Sasakian manifold to its tangent bundle, Mathematics, 11(2023), 53.
  • Liang, Y., On semi-symmetric recurrent-metric connection, Tensor N. S., 55 (1994), 107–112.
  • Mondal, A.K., De, U.C., Some properties of a quarter-symmetric metric connection on a Sasakian manifold, Bulletin of Mathematical analysis and applications, 1(2)(2009), 99–108.
  • Mukhopadhyay, S. , Roy, A.K. Barua, B., Some properties of a quarter-symmetric metric connection on a Riemannian manifold, Soochow J. of Math., 17(2)(1991), 205–211.
  • Sular, S., Ozgur, C. and De, U. C., Quarter-symmetric metric connection in a Kenmotsu manifold, SUT Journal of mathematics, 44( 2) (2008), 297-306.
  • Tani, M., Prolongations of hypersurfaces of tangent bundles, Kodai Math. Semp. Rep., 21 (1969), 85-96.
  • Yano, K. and Ishihara, S., Tangent and cotangent bundles, Marcel Dekker Inc., New York, 1973.

On Tangent Bundles of Submanifolds of a Riemannian Manifold Endowed with a Quarter-Symmetric Non-metric Connection

Yıl 2023, Cilt: 15 Sayı: 2, 355 - 364, 31.12.2023
https://doi.org/10.47000/tjmcs.1355887

Öz

The object of this article is to study a quarter-symmetric non-metric connection in the tangent bundle and induced metric and connection on submanifold of co-dimension 2 and hypersurface concerning the quarter-symmetric non-metric connection in the tangent bundle. The Weingarten equations concerning the quarter-symmetric non-metric connection on a submanifold of co-dimension 2 and the hypersurface in the tangent bundle are obtained. Finally, authors deduce the Riemannian curvature tensor and Gauss and Codazzi equations on a submanifold of co-dimension 2 and hypersurface of the Riemannian manifold concerning the quarter-symmetric non-metric connection in the tangent bundle.

Kaynakça

  • Altunbas, M., Bilen, L.,Gezer, A., Remarks about the Kaluza-Klein metric on tangent bundle, Int. J. Geo. Met. Mod. Phys., 16(3)(2019), 1950040.
  • Azami, S., General natural metallic structure on tangent bundle, Iran J Sci Technol Trans Sci, 42(2018), 81—88.
  • Ali, S., Nivas, R., On submanifolds immersed in a manifold with quarter symmetric connection, Riv. Mat. Univ. Parma., 6(3)(2000), 11–23.
  • Bahadir, O., Lorentzian para-Sasakian manifold with quarter-symmetric non-metric connection, Journal of Dynamical Systems and Geometric Theories, 14(1)(2016), 17–33.
  • Bilen, L., Turanli, S., Gezer, A., On K¨ahler–Norden–Codazzi golden structures on pseudo-Riemannian manifolds, International Journal of Geometric Methods in Modern Physics, 15(2018), 1–10.
  • Chaubey, S.K., De, U.C., Characterization of the Lorentzian para-Sasakian manifolds admitting a quarter-symmetric non-metric connection, SUT Journal of Mathematics, 55(1)(2019), 53–67.
  • Choudhary, M.A., Khan, M.N.I., Siddiqi, M.D., Some basic inequalities on (ϵ)-Para Sasakian manifold, Symmetry, 14(12)(2022), 2585.
  • Das, L.S., Second order parallel tensors on para r-Sasakian manifolds with coefficient α, Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis, 28(2012), 83–88.
  • Das, L.S., Second order parallel tensor on α- Sasakian manifold, Acta Mathematica, Academiae Pedagogicae Nyiregyhaziensis, 23(1)(2007), 65–69.
  • Das, L.S., Khan, M.N.I., Symmetric and Ricci LP-Sasakian manifold, Mathematical Sciences Research Journal, 17(10)(2013), 263–268.
  • Das, L.S., Nivas, R., Khan, M.N.I., On Semi-invariant submanifolds of conformal K(ξ) contact Riemannian manifold, Algebras, Groups and Geometries, 23(1)(2006), 292–302.
  • De, U.C., Kamilya, D., Hypersurfaces of Rieamnnian manifold with semi-symmetric non-metric connection, J. Indian Inst. Sci., 75(1995), 707–710.
  • De, U.C., Mondal, A.K., Hypersurfaces of Kenmotsu manifolds endowed with a quarter-symmetric non-metric connection, Kuwait J. Sci. Eng., 39(2012), 43–56.
  • De, U.C., Mandal, D., Mandal, K., Some characterizations of Kenmotsu manifolds admitting a quarter-symmetric metric connection, Bull.Transilv. Univ. Bra¸sov Ser. III, 9(58)(1)(2016), 39–52.
  • Dida, H.M., Hathout, F., Ricci soliton on the tangent bundle with semi-symmetric metric connection, Bulletin of the Transilvania University of Brasov Series III: Mathematics and Computer Science, 1(63)(2)(2021), 37–52.
  • Dida, H.M., Ikemakhen, A., A class of metrics on tangent bundles of pseudo-Riemannian manifolds, Archivum Mathematicum (BRNO) Tomus, 47(2011), 293—308.
  • Dida, H.M., Hathout, F., Djaa, M., On the geometry of the second order tangent bundle with the diagonal lift metric, Int. Journal of Math. Analysis, 3(9)(2009), 443–456.
  • Friedmann, A., Schouten, J.A. , A¨Uber die geometrie der halbsymmetrischen A¨ubertragung, Math. Zeitschr., 21(1924), 211–223.
  • Golab, S., On semi-symmetric and quarter-symmetric linear connections, Tensor, N. S., 29(1975), 249–254.
  • Hayden, H.A., Subspaces of a space with torsion, Proc. London Math. Soc., 34(1932), 27–50.
  • Han, Y., Yun, H.T., Zhao, P., Some invariants of quarter-symmetric metric connections under the projective transformation, Filomat, 27(4)(2013), 679–691.
  • Kazan, A., Karadag, H.B., Locally decomposable golden tangent bundles with CheegerGromoll metric, Miskolc Math. Not., 17(1)(2016), 399–411.
  • Khan, M.N.I., Proposed theorems for lifts of the extended almost complex structures on the complex manifold, Asian-European Journal of Mathematics, 15(11)(2022), 2250200.
  • Khan, M.N.I., Novel theorems for the frame bundle endowed with metallic structures on an almost contact metric manifold, Chaos, Solitons & Fractals, 146(2021), 110872.
  • Khan, M.N.I., De, U.C., Liftings of metallic structures to tangent bundles of order r, AIMS Mathematics, 7(5)(2022), 7888–7897.
  • Khan, M.N.I., Das, L.S., On CR-structure and the general quadratic structure, Journal for Geometry and Graphics, 24(2)(2020), 249–255.
  • Khan, M.N.I., Jun, J.B., Covariant derivative of certain structures in tangent bundle, Journal of the Chungcheong Mathematical Society, 30(4)(2017), 387–396.
  • Khan, M.N.I., Choudhary, M.A., Chaubey, S.K., Alternative Equations for Horizontal Lifts of the Metallic Structures from Manifold onto Tangent Bundle, Journal of Mathematics, 2022(Article ID 5037620)(2022).
  • Khan, M.N.I., Submanifolds of a Riemannian manifold endowed with a new type of semi-symmetric non-metric connection in the tangent bundle, International Journal of Mathematics and Computer Science, 17(1)(2022), 265-–275.
  • Khan, M.N.I., Mofarreh, F., Haseeb, A., Tangent bundles of P-Sasakian manifolds endowed with a quarter-symmetric metric connection, Symmetry, 15(3)(2023), 753.
  • Khan, M.N.I., A note on certain structures in the tangent bundle, Far East Journal of Mathematical Sciences, 101(9)(2017), 1947–1965.
  • Khan, M.N.I., Mofarreh, F., Haseeb, A., Saxena, M., Certain results on the lifts from an LP-Sasakian manifold to its tangent bundle associated with a quarter-symmetric metric connection, Symmetry, 15(8)(2023), 1553.
  • Khan, M.N.I., De, U.C., Lifts of metallic structure on a cross section, Filomat, 36(18)(2023), 6369–6363.
  • Khan, M.N.I., Liftings from a Para-Sasakian manifold to its tangent bundles, Filomat, 37(20)(2023), 6727–6740.
  • Khan, M.N.I., Novel theorems for metallic structures on the frame bundle of the second order, Filomat, 36(13)(2022), 4471–4482.
  • Khan, M.N.I., De, U.C., Velimirovic, L.S., Lifts of a quarter-symmetric metric connection from a Sasakian manifold to its tangent bundle, Mathematics, 11(2023), 53.
  • Liang, Y., On semi-symmetric recurrent-metric connection, Tensor N. S., 55 (1994), 107–112.
  • Mondal, A.K., De, U.C., Some properties of a quarter-symmetric metric connection on a Sasakian manifold, Bulletin of Mathematical analysis and applications, 1(2)(2009), 99–108.
  • Mukhopadhyay, S. , Roy, A.K. Barua, B., Some properties of a quarter-symmetric metric connection on a Riemannian manifold, Soochow J. of Math., 17(2)(1991), 205–211.
  • Sular, S., Ozgur, C. and De, U. C., Quarter-symmetric metric connection in a Kenmotsu manifold, SUT Journal of mathematics, 44( 2) (2008), 297-306.
  • Tani, M., Prolongations of hypersurfaces of tangent bundles, Kodai Math. Semp. Rep., 21 (1969), 85-96.
  • Yano, K. and Ishihara, S., Tangent and cotangent bundles, Marcel Dekker Inc., New York, 1973.
Toplam 42 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Cebirsel ve Diferansiyel Geometri
Bölüm Makaleler
Yazarlar

Mohammad Nazrul Islam Khan 0000-0002-9652-0355

Lovejoy Das 0000-0002-2709-5113

Yayımlanma Tarihi 31 Aralık 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 15 Sayı: 2

Kaynak Göster

APA Khan, M. N. I., & Das, L. (2023). On Tangent Bundles of Submanifolds of a Riemannian Manifold Endowed with a Quarter-Symmetric Non-metric Connection. Turkish Journal of Mathematics and Computer Science, 15(2), 355-364. https://doi.org/10.47000/tjmcs.1355887
AMA Khan MNI, Das L. On Tangent Bundles of Submanifolds of a Riemannian Manifold Endowed with a Quarter-Symmetric Non-metric Connection. TJMCS. Aralık 2023;15(2):355-364. doi:10.47000/tjmcs.1355887
Chicago Khan, Mohammad Nazrul Islam, ve Lovejoy Das. “On Tangent Bundles of Submanifolds of a Riemannian Manifold Endowed With a Quarter-Symmetric Non-Metric Connection”. Turkish Journal of Mathematics and Computer Science 15, sy. 2 (Aralık 2023): 355-64. https://doi.org/10.47000/tjmcs.1355887.
EndNote Khan MNI, Das L (01 Aralık 2023) On Tangent Bundles of Submanifolds of a Riemannian Manifold Endowed with a Quarter-Symmetric Non-metric Connection. Turkish Journal of Mathematics and Computer Science 15 2 355–364.
IEEE M. N. I. Khan ve L. Das, “On Tangent Bundles of Submanifolds of a Riemannian Manifold Endowed with a Quarter-Symmetric Non-metric Connection”, TJMCS, c. 15, sy. 2, ss. 355–364, 2023, doi: 10.47000/tjmcs.1355887.
ISNAD Khan, Mohammad Nazrul Islam - Das, Lovejoy. “On Tangent Bundles of Submanifolds of a Riemannian Manifold Endowed With a Quarter-Symmetric Non-Metric Connection”. Turkish Journal of Mathematics and Computer Science 15/2 (Aralık 2023), 355-364. https://doi.org/10.47000/tjmcs.1355887.
JAMA Khan MNI, Das L. On Tangent Bundles of Submanifolds of a Riemannian Manifold Endowed with a Quarter-Symmetric Non-metric Connection. TJMCS. 2023;15:355–364.
MLA Khan, Mohammad Nazrul Islam ve Lovejoy Das. “On Tangent Bundles of Submanifolds of a Riemannian Manifold Endowed With a Quarter-Symmetric Non-Metric Connection”. Turkish Journal of Mathematics and Computer Science, c. 15, sy. 2, 2023, ss. 355-64, doi:10.47000/tjmcs.1355887.
Vancouver Khan MNI, Das L. On Tangent Bundles of Submanifolds of a Riemannian Manifold Endowed with a Quarter-Symmetric Non-metric Connection. TJMCS. 2023;15(2):355-64.