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Some Curves on alpha-para Kenmotsu manifolds with semisymmetric metric connections.

Yıl 2018, Cilt: 6 Sayı: 2, 299 - 305, 15.10.2018

Öz

The object of the present paper is to study biharmonic almost contact curves on three-dimensional alpha-para Kenmotsu manifolds with respect to semisymmetric metric connections. With respect to semisymmetric metric connection slant curves have been analysed. Locally phi-symmetric Legendre curves with respect to semisymmetric metric connections have also been considered. An example is given


Kaynakça

  • [1] Baikoussis, C. and Blair, D. E., On Legendre curves in contact 3-manifolds Geom. Dedicata, 49(1994), 135-142.
  • [2] Barman, A., On Lorentzian a-Sasakian manifolds admitting a type of semisymmetric metric connection, Novi Sad J. Math. 44(2014), 77-88.
  • [3] Blair, D. E., Contact manifolds in Riemannian Geometry, Lecture notes in Math 509, Springer-Verlag, Berlin-Heidelberg-New York(1976).
  • [4] Blair, D. E., Kim, J. S. and Tripathi, M. M., On the concircular curvature tensor of a contact metric manifold, J. Korean Math. Soc. 42(2005), 883-892.
  • [5] Caddeo, R., Montaldo, S. and Piu, P., Biharmonic curves on a surface, Rend, Mat. Appl. 21(2001), no.1-4, 143-157.
  • [6] Calin, C. and Crasmareanu, M., Slant curves in 3-dimensional Normal Almost Contact Geometry, Mediterr. J. Math. 10(2013), 1067-1077.
  • [7] Cappelletti-Montano, B., Bi-Legendrian structures and paracontact geometry, Int. J. Geom. Meth. Mod. Phys. 6(2009), 487-504.
  • [8] Chinea, D. and Gonzales, C., A classification of almost contact metric manifolds, Ann. Mat. Pure Appl., 156(1990), 15-36.
  • [9] Cho, J. T., Inoguchi, J. I. and Lee, J. E., On slant curves in Sasakian space forms, J. Korean Math. Soc. 74(2006), 359-367.
  • [10] Cho, J. T. and Lee, J. E., Slant curves in contact Pseudo-Hermitian manifolds, Bull. Austral. Math. Soc., 78(2008), 383-396.
  • [11] Erdem, S., On almost (para) contact (hyperbolic) metric manifolds and harmonicity of (f;f0 )-holomorphic maps between them, Houston J. Math. 28(2002), 21-45.
  • [12] Fetcu, D., Biharmonic Legendre curves in Sasakian space forms, J. Korean Math. Soc. 45(2008), 393-404.
  • [13] Friedmann, A. and Schouten, ¨U berdie Geometrie der halbsymmetrischen ¨U bertragung, Math.Z., 21(1924), 211-223.
  • [14] Hayden, H. A., Subspaces of space with torsion, Proc. London Math. Soc., 34(1932), 27-50.
  • [15] Inoguchi, J. I. and Lee, J. E., Affine biharmonic curves in 3-dimensional homogeneous geometries, Mediterr. J. Math. 10(2013), 571-592.
  • [16] Inoguchi, J. I. and Lee, J. E., On slant curves in normal almost contact metric 3-manifolds, Beitr. Algebra Geom. 55(2014), 603-620.
  • [17] Janssens, D. and Vanhecke, L., Almost contact structures and curvature tensors, Kodai. Math. J. 4(1981), 1-27.
  • [18] Kaneyuki, S. and Williams, F. L., Almost paracontact and parahodge structures on manifolds, Nagoya Math. J. 99(1985), 173-187.
  • [19] Majhi, P., A note on a-para Kenmotsu manifolds, Facta Universitatis, 31(2016), 227-236.
  • [20] Montaldo, S. and Oniciuc, C., A short survey on biharmonic maps between Riemannian manifolds, Revista De La Union Matematica Argentina, 47(2006), 1-22.
  • [21] Olszak, Z., Normal almost contact metric manifolds of dimension three, Ann. Polon. Math. 47(1986), 41-50.
  • [22] Oubina, J. A., New classes of alomost contact metric structures, Publ. Math. Debrecen, 32(1985), 187-193.
  • [23] P, Dacko., On almost para-cosymplectic manifolds, Tsukuba J. Math. 28(2004), 193-213.
  • [24] Sarkar, A. and Biswas, D., Legendre curves on three dimensional Heisenberg Groups, Facta Universitatis, 28(2013), 241-248.
  • [25] Sarkar, A., Mondal, A. and Biswas, D., Some curves on three-dimensional trans-Sasakian manifolds with semisymmetric metric connection, Palest. J. Math., 5(2016), 195-203.
  • [26] Sarkar, A. and Mondal, A., Certain curves on some classes of three-dimensional almost contact metric manifolds, Revista de La Union Mat. Argentina, 58(2017), 107-125.
  • [27] Sarkar, A. and Sil, Amit, Legendre curves on three-dimensional quasi-Sasakian manifolds with semisymmetric metric connection, Acta Mathematica Academiae Paedagogiace Nyiregyhaziensis,(to appear, 2017).
  • [28] Sarkar, A. and Sil, Amit, Curves on some classes of Kenmotsu manifolds, Ann. Univ. Sci Budapest, 59(2016), 101-112.
  • [29] Sarkar, A. and Sil, Amit, Certain curves on a-para Kenmotsu manifolds, (communicated)
  • [30] Schouten, J. A.: Ricci Calculus, An Introduction to Tensor Analysis and Its Geometrical Applications, Springer-Verlag, Berlin, 1954
  • [31] Sharfuddin, A. and Hussain, S. I., Semi Symmetric metric connections in almost contact manifolds, Tensor, New Ser. 30(1976), 133-139.
  • [32] Srivastava, K. and Srivastava, S. K., On a class of a-para Kenmotsu manifolds, Mediterr. J. Math. 13(2016), 391-399.
  • [33] Welyczko, J., On Legendre curves in 3-dimensional normal almost contact metric manifolds, Soochow J. Math., 33(2007), 929-937.
  • [34] Welyczko, J., Slant curves in 3-dimensional normal almost paracontact metric manifolds, Mediterr. J. Math, 11(2014), 965-978.
  • [35] Yano, K., On Semi Symmetric connection, Rev. Roum, Math. Pure Appl., 15(1970), 1570-1586.
  • [36] Zamkovoy, S., Canonical connections on paracontact manifolds, Ann. Glob. Anal. Geom.36(1)(2009), 37-60.
Yıl 2018, Cilt: 6 Sayı: 2, 299 - 305, 15.10.2018

Öz

Kaynakça

  • [1] Baikoussis, C. and Blair, D. E., On Legendre curves in contact 3-manifolds Geom. Dedicata, 49(1994), 135-142.
  • [2] Barman, A., On Lorentzian a-Sasakian manifolds admitting a type of semisymmetric metric connection, Novi Sad J. Math. 44(2014), 77-88.
  • [3] Blair, D. E., Contact manifolds in Riemannian Geometry, Lecture notes in Math 509, Springer-Verlag, Berlin-Heidelberg-New York(1976).
  • [4] Blair, D. E., Kim, J. S. and Tripathi, M. M., On the concircular curvature tensor of a contact metric manifold, J. Korean Math. Soc. 42(2005), 883-892.
  • [5] Caddeo, R., Montaldo, S. and Piu, P., Biharmonic curves on a surface, Rend, Mat. Appl. 21(2001), no.1-4, 143-157.
  • [6] Calin, C. and Crasmareanu, M., Slant curves in 3-dimensional Normal Almost Contact Geometry, Mediterr. J. Math. 10(2013), 1067-1077.
  • [7] Cappelletti-Montano, B., Bi-Legendrian structures and paracontact geometry, Int. J. Geom. Meth. Mod. Phys. 6(2009), 487-504.
  • [8] Chinea, D. and Gonzales, C., A classification of almost contact metric manifolds, Ann. Mat. Pure Appl., 156(1990), 15-36.
  • [9] Cho, J. T., Inoguchi, J. I. and Lee, J. E., On slant curves in Sasakian space forms, J. Korean Math. Soc. 74(2006), 359-367.
  • [10] Cho, J. T. and Lee, J. E., Slant curves in contact Pseudo-Hermitian manifolds, Bull. Austral. Math. Soc., 78(2008), 383-396.
  • [11] Erdem, S., On almost (para) contact (hyperbolic) metric manifolds and harmonicity of (f;f0 )-holomorphic maps between them, Houston J. Math. 28(2002), 21-45.
  • [12] Fetcu, D., Biharmonic Legendre curves in Sasakian space forms, J. Korean Math. Soc. 45(2008), 393-404.
  • [13] Friedmann, A. and Schouten, ¨U berdie Geometrie der halbsymmetrischen ¨U bertragung, Math.Z., 21(1924), 211-223.
  • [14] Hayden, H. A., Subspaces of space with torsion, Proc. London Math. Soc., 34(1932), 27-50.
  • [15] Inoguchi, J. I. and Lee, J. E., Affine biharmonic curves in 3-dimensional homogeneous geometries, Mediterr. J. Math. 10(2013), 571-592.
  • [16] Inoguchi, J. I. and Lee, J. E., On slant curves in normal almost contact metric 3-manifolds, Beitr. Algebra Geom. 55(2014), 603-620.
  • [17] Janssens, D. and Vanhecke, L., Almost contact structures and curvature tensors, Kodai. Math. J. 4(1981), 1-27.
  • [18] Kaneyuki, S. and Williams, F. L., Almost paracontact and parahodge structures on manifolds, Nagoya Math. J. 99(1985), 173-187.
  • [19] Majhi, P., A note on a-para Kenmotsu manifolds, Facta Universitatis, 31(2016), 227-236.
  • [20] Montaldo, S. and Oniciuc, C., A short survey on biharmonic maps between Riemannian manifolds, Revista De La Union Matematica Argentina, 47(2006), 1-22.
  • [21] Olszak, Z., Normal almost contact metric manifolds of dimension three, Ann. Polon. Math. 47(1986), 41-50.
  • [22] Oubina, J. A., New classes of alomost contact metric structures, Publ. Math. Debrecen, 32(1985), 187-193.
  • [23] P, Dacko., On almost para-cosymplectic manifolds, Tsukuba J. Math. 28(2004), 193-213.
  • [24] Sarkar, A. and Biswas, D., Legendre curves on three dimensional Heisenberg Groups, Facta Universitatis, 28(2013), 241-248.
  • [25] Sarkar, A., Mondal, A. and Biswas, D., Some curves on three-dimensional trans-Sasakian manifolds with semisymmetric metric connection, Palest. J. Math., 5(2016), 195-203.
  • [26] Sarkar, A. and Mondal, A., Certain curves on some classes of three-dimensional almost contact metric manifolds, Revista de La Union Mat. Argentina, 58(2017), 107-125.
  • [27] Sarkar, A. and Sil, Amit, Legendre curves on three-dimensional quasi-Sasakian manifolds with semisymmetric metric connection, Acta Mathematica Academiae Paedagogiace Nyiregyhaziensis,(to appear, 2017).
  • [28] Sarkar, A. and Sil, Amit, Curves on some classes of Kenmotsu manifolds, Ann. Univ. Sci Budapest, 59(2016), 101-112.
  • [29] Sarkar, A. and Sil, Amit, Certain curves on a-para Kenmotsu manifolds, (communicated)
  • [30] Schouten, J. A.: Ricci Calculus, An Introduction to Tensor Analysis and Its Geometrical Applications, Springer-Verlag, Berlin, 1954
  • [31] Sharfuddin, A. and Hussain, S. I., Semi Symmetric metric connections in almost contact manifolds, Tensor, New Ser. 30(1976), 133-139.
  • [32] Srivastava, K. and Srivastava, S. K., On a class of a-para Kenmotsu manifolds, Mediterr. J. Math. 13(2016), 391-399.
  • [33] Welyczko, J., On Legendre curves in 3-dimensional normal almost contact metric manifolds, Soochow J. Math., 33(2007), 929-937.
  • [34] Welyczko, J., Slant curves in 3-dimensional normal almost paracontact metric manifolds, Mediterr. J. Math, 11(2014), 965-978.
  • [35] Yano, K., On Semi Symmetric connection, Rev. Roum, Math. Pure Appl., 15(1970), 1570-1586.
  • [36] Zamkovoy, S., Canonical connections on paracontact manifolds, Ann. Glob. Anal. Geom.36(1)(2009), 37-60.
Toplam 36 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Amit Sil

Avijit Sarkar

Yayımlanma Tarihi 15 Ekim 2018
Gönderilme Tarihi 16 Haziran 2017
Kabul Tarihi 27 Kasım 2017
Yayımlandığı Sayı Yıl 2018 Cilt: 6 Sayı: 2

Kaynak Göster

APA Sil, A., & Sarkar, A. (2018). Some Curves on alpha-para Kenmotsu manifolds with semisymmetric metric connections. Konuralp Journal of Mathematics, 6(2), 299-305.
AMA Sil A, Sarkar A. Some Curves on alpha-para Kenmotsu manifolds with semisymmetric metric connections. Konuralp J. Math. Ekim 2018;6(2):299-305.
Chicago Sil, Amit, ve Avijit Sarkar. “Some Curves on Alpha-Para Kenmotsu Manifolds With Semisymmetric Metric Connections”. Konuralp Journal of Mathematics 6, sy. 2 (Ekim 2018): 299-305.
EndNote Sil A, Sarkar A (01 Ekim 2018) Some Curves on alpha-para Kenmotsu manifolds with semisymmetric metric connections. Konuralp Journal of Mathematics 6 2 299–305.
IEEE A. Sil ve A. Sarkar, “Some Curves on alpha-para Kenmotsu manifolds with semisymmetric metric connections”., Konuralp J. Math., c. 6, sy. 2, ss. 299–305, 2018.
ISNAD Sil, Amit - Sarkar, Avijit. “Some Curves on Alpha-Para Kenmotsu Manifolds With Semisymmetric Metric Connections”. Konuralp Journal of Mathematics 6/2 (Ekim 2018), 299-305.
JAMA Sil A, Sarkar A. Some Curves on alpha-para Kenmotsu manifolds with semisymmetric metric connections. Konuralp J. Math. 2018;6:299–305.
MLA Sil, Amit ve Avijit Sarkar. “Some Curves on Alpha-Para Kenmotsu Manifolds With Semisymmetric Metric Connections”. Konuralp Journal of Mathematics, c. 6, sy. 2, 2018, ss. 299-05.
Vancouver Sil A, Sarkar A. Some Curves on alpha-para Kenmotsu manifolds with semisymmetric metric connections. Konuralp J. Math. 2018;6(2):299-305.
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