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Year 2020, Volume: 8 Issue: 1, 152 - 157, 15.04.2020

Abstract

References

  • [1] A. Bejancu and H. R. Faran, Foliations and Geometric Structures, Math. and Its Appl. 580, Springer, Dordrecht, 2006.
  • [2] D. E. Blair, Contact Manifolds in Riemannian Geometry, Lecture Notes in Mathematics. 509, Springer-Verlag, Berlin-New York, 1976.
  • [3] D. E. Blair and J. A. Oubina, Conformal and related changes of metric on the product of two almost contact metric manifolds, Publications Matematiques, 34 (1990), 199-207.
  • [4] D. Chinea and C. Gonzales, A classification of almost contact metric manifolds, Ann. Mat. Pura Appl., 156 (1990), 15-36.
  • [5] U. C. De and M. M. Tripathi, Ricci tensor in 3-dimensional trans-Sasakian manifolds, Kyungpook Math. J., 43 (2003), 247-255.
  • [6] A. Gray and L. M. Hervella, The sixteen classes of almost Hermitian manifolds and their linear invariants, Ann. Mat. Pura Appl., 123 (1980), 35-58.
  • [7] S. Ianus¸, Some almost product structures on manifolds with linear connection, Kodai Math. Sem. Rep., 23 (1971), 305-310.
  • [8] D. Janssens and L. Vanhecke, Almost contact structures and curvature tensors, Kodai Math. J., 4 (1981), 1-27.
  • [9] A. Kazan and H. B. Karada˜g, Trans-Sasakian manifolds with Schouten-van Kampen Connection, Ilirias Journal of Mathematics, 7 (2018), 1-12.
  • [10] J. C. Marrero, The local structure of trans-Sasakian manifolds, Ann. Mat. Pura Appl., 162 (1992), 77-86.
  • [11] J. C. Marrero and D. Chinea, On trans-Sasakian manifolds, in Proceedings of the XIVth Spanish-Portuguese Conference on Mathematics, Vol. 1, 1989.
  • [12] J. A. Oubina, New classes of almost contact metric structures, Publ. Mat. Debrecen, 32(1985), 187-193.
  • [13] Z. Olszak, The Schouten-van Kampen affine connection adapted an almost (para) contact metric structure, Publ. De L’inst. Math., 94 (2013), 31-42.
  • [14] J. Schouten and E. van Kampen, Zur Einbettungs-und Kr¨ummungsthorie nichtholonomer Gebilde, Math. Ann., 103 (1930), 752-783.
  • [15] A. F. Solov’ev, On the curvature of the connection induced on a hyperdistribution in a Riemannian space, Geom. Sb., 19 (1978), 12-23.
  • [16] A. F. Solov’ev, The bending of hyperdistributions, Geom. Sb., 20 (1979), 101-112.
  • [17] A. F. Solov’ev, Second fundamental form of a distribution, Mathematical notes of the Academy of Sciences of the USSR, 31 (1982), 71-75.
  • [18] A. F. Solov’ev, Curvature of a distribution, Mathematical notes of the Academy of Sciences of the USSR, 35 (1984), 61-68.
  • [19] A. Yıldız, f-Kenmotsu manifolds with the Schouten-van Kampen connection, Publ. de I’Inst. Math., 102 (2017), 93-105.

On Trans-Sasakian Manifolds with the Schouten-van Kampen Connection

Year 2020, Volume: 8 Issue: 1, 152 - 157, 15.04.2020

Abstract

The object of the present paper is to characterize $3$-dimensional trans-Sasakian manifolds with respect to the Schouten-van Kampen connection.

References

  • [1] A. Bejancu and H. R. Faran, Foliations and Geometric Structures, Math. and Its Appl. 580, Springer, Dordrecht, 2006.
  • [2] D. E. Blair, Contact Manifolds in Riemannian Geometry, Lecture Notes in Mathematics. 509, Springer-Verlag, Berlin-New York, 1976.
  • [3] D. E. Blair and J. A. Oubina, Conformal and related changes of metric on the product of two almost contact metric manifolds, Publications Matematiques, 34 (1990), 199-207.
  • [4] D. Chinea and C. Gonzales, A classification of almost contact metric manifolds, Ann. Mat. Pura Appl., 156 (1990), 15-36.
  • [5] U. C. De and M. M. Tripathi, Ricci tensor in 3-dimensional trans-Sasakian manifolds, Kyungpook Math. J., 43 (2003), 247-255.
  • [6] A. Gray and L. M. Hervella, The sixteen classes of almost Hermitian manifolds and their linear invariants, Ann. Mat. Pura Appl., 123 (1980), 35-58.
  • [7] S. Ianus¸, Some almost product structures on manifolds with linear connection, Kodai Math. Sem. Rep., 23 (1971), 305-310.
  • [8] D. Janssens and L. Vanhecke, Almost contact structures and curvature tensors, Kodai Math. J., 4 (1981), 1-27.
  • [9] A. Kazan and H. B. Karada˜g, Trans-Sasakian manifolds with Schouten-van Kampen Connection, Ilirias Journal of Mathematics, 7 (2018), 1-12.
  • [10] J. C. Marrero, The local structure of trans-Sasakian manifolds, Ann. Mat. Pura Appl., 162 (1992), 77-86.
  • [11] J. C. Marrero and D. Chinea, On trans-Sasakian manifolds, in Proceedings of the XIVth Spanish-Portuguese Conference on Mathematics, Vol. 1, 1989.
  • [12] J. A. Oubina, New classes of almost contact metric structures, Publ. Mat. Debrecen, 32(1985), 187-193.
  • [13] Z. Olszak, The Schouten-van Kampen affine connection adapted an almost (para) contact metric structure, Publ. De L’inst. Math., 94 (2013), 31-42.
  • [14] J. Schouten and E. van Kampen, Zur Einbettungs-und Kr¨ummungsthorie nichtholonomer Gebilde, Math. Ann., 103 (1930), 752-783.
  • [15] A. F. Solov’ev, On the curvature of the connection induced on a hyperdistribution in a Riemannian space, Geom. Sb., 19 (1978), 12-23.
  • [16] A. F. Solov’ev, The bending of hyperdistributions, Geom. Sb., 20 (1979), 101-112.
  • [17] A. F. Solov’ev, Second fundamental form of a distribution, Mathematical notes of the Academy of Sciences of the USSR, 31 (1982), 71-75.
  • [18] A. F. Solov’ev, Curvature of a distribution, Mathematical notes of the Academy of Sciences of the USSR, 35 (1984), 61-68.
  • [19] A. Yıldız, f-Kenmotsu manifolds with the Schouten-van Kampen connection, Publ. de I’Inst. Math., 102 (2017), 93-105.
There are 19 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Semra Zeren 0000-0003-0083-3507

Ahmet Yıldız

Publication Date April 15, 2020
Submission Date December 3, 2019
Acceptance Date March 28, 2020
Published in Issue Year 2020 Volume: 8 Issue: 1

Cite

APA Zeren, S., & Yıldız, A. (2020). On Trans-Sasakian Manifolds with the Schouten-van Kampen Connection. Konuralp Journal of Mathematics, 8(1), 152-157.
AMA Zeren S, Yıldız A. On Trans-Sasakian Manifolds with the Schouten-van Kampen Connection. Konuralp J. Math. April 2020;8(1):152-157.
Chicago Zeren, Semra, and Ahmet Yıldız. “On Trans-Sasakian Manifolds With the Schouten-Van Kampen Connection”. Konuralp Journal of Mathematics 8, no. 1 (April 2020): 152-57.
EndNote Zeren S, Yıldız A (April 1, 2020) On Trans-Sasakian Manifolds with the Schouten-van Kampen Connection. Konuralp Journal of Mathematics 8 1 152–157.
IEEE S. Zeren and A. Yıldız, “On Trans-Sasakian Manifolds with the Schouten-van Kampen Connection”, Konuralp J. Math., vol. 8, no. 1, pp. 152–157, 2020.
ISNAD Zeren, Semra - Yıldız, Ahmet. “On Trans-Sasakian Manifolds With the Schouten-Van Kampen Connection”. Konuralp Journal of Mathematics 8/1 (April 2020), 152-157.
JAMA Zeren S, Yıldız A. On Trans-Sasakian Manifolds with the Schouten-van Kampen Connection. Konuralp J. Math. 2020;8:152–157.
MLA Zeren, Semra and Ahmet Yıldız. “On Trans-Sasakian Manifolds With the Schouten-Van Kampen Connection”. Konuralp Journal of Mathematics, vol. 8, no. 1, 2020, pp. 152-7.
Vancouver Zeren S, Yıldız A. On Trans-Sasakian Manifolds with the Schouten-van Kampen Connection. Konuralp J. Math. 2020;8(1):152-7.
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