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Year 2019, Volume: 12 Issue: 1, 71 - 84, 27.03.2019

Haşim Çayır , Fıdan Jabrailzade

https://doi.org/10.36890/iejg.545763
Cited By: 1

Abstract

References

  • [1] Akyol, M. A. and Gündüzalp, Y., Hemi-Slant Submersions from Almost Product Riemannian Manifolds. Gulf Journal of Mathematics 4 (2016), no. 3, 15-27.
  • [2] Akyol, M. A. and Gündüzalp, Y., Hemi-Invariant Semi-Riemannian Submersions. Commun. Fac. Sci. Univ. Ank. Series A1 67 (2018), no. 1, 80-92.
  • [3] Andreou, F. G., On integrability conditions of a structure f satisfying f5 + f = 0. Tensor, N.S. 40 (1983), 27-31.
  • [4] Cengiz, N. and Salimov, A. A., Diagonal Lift in the Tensor Bundle and its Applications. Applied Mathematics and Computation 142 (2003) 309-319.
  • [5] Çayır, H., Some Notes on Lifts of Almost Paracontact Structures. American Review of Mathematics and Statistics 3 (2015), no. 1, 52-60.
  • [6] Çayır, H., Lie derivatives of almost contact structure and almost paracontact structure with respect to XV and XH on tangent bundle T(M). Proceedings of the Institute of Mathematics and Mechanics 42 (2016), no. 1, 38-49.
  • [7] Çayır, H., Tachibana and Vishnevskii Operators Applied to XV and XH in Almost Paracontact Structure on Tangent Bundle T(M). New Trends in Mathematical Sciences 4 (2016), no. 3, 105-115.
  • [8] Çayır, H. and Köseoğlu, G., Lie Derivatives of Almost Contact Structure and Almost Paracontact Structure With Respect to XC and XV on Tangent Bundle T(M). New Trends in Mathematical Sciences 4 (2016), no. 1, 153-159.
  • [9] Das, L., On CR-structure and an f(2K + 4; 2)-structure satisfying f^(2K+4)+ f^2 = 0. Tensor 73 (2011), no. 3, 222-227.
  • [10] Das, L., On lifts of structure satisfying F^( K+1)− a^2 F^(K−1). Kyungpook Mathematical Journal 40 (2000), no. 2, 391-398.
  • [11] Gupta, V.C., Integrability Conditions of a Structure F Satisfying F^K + F = 0: The Nepali Math. Sc. Report 14 (1998), no. 2, 55-62.
  • [12] Ishıhara, S. and Yano, K., On integrability conditions of a structure f satisfying f^3 + f = 0: Quaterly J. Math. 15 (1964), 217-222.
  • [13] Kobayashi, S. and Nomizu, K., Foundations of Differential Geometry-Volume I. John Wiley & Sons, Inc, New York, 1963.
  • [14] Lovejoy, S. D., Nivas, R. and Pathak, V. N., On horizontal and complete lifts from a manifold with fλ(7; 1)-structure to its cotangent bundle. International Journal of Mathematics and Mathematical Sciences 8 (2005), 1291-1297.
  • [15] Musso, E. and Tricerri, F., Riemannian Metric on Tangent Bundles. Ann. Math. Pura. Appl. 150 (1988), no. 4, 1-9.
  • [16] Nivas, R. and Prasad, C. S., On a structure defined by a tensor field f(≠ 0) of type (1; 1) satisfying f^5 - a^2 f = 0. Nep. Math. Sc. Rep. 10 (1985), no. 1, 25-30.
  • [17] Sahin, B.,Anti-invariant Riemannian submersions from almost Hermitian manifolds. CentralEuropean J.Math. 3 (2010), 437-447.
  • [18] Sahin, B., Semi-invariant Riemannian submersions from almost Hermitian manifolds. Canad.Math. Bull. 56 (2013), 173-183.
  • [19] Salimov, A. A., Tensor Operators and Their applications. Nova Science Publ., New York, 2013.
  • [20] Salimov, A. A. and Çayır, H., Some Notes On Almost Paracontact Structures. C. R. Acad. Bulgare Sci. 66 (2013), no. 3, 331-338.
  • [21] Singh, A., On CR􀀀structures F􀀀structures satisfying F^(2K+P) + F^P = 0. Int. J. Contemp. Math. Sciences 4 (2009), 1029-1035.
  • [22] Singh, A., Pandey, R. K. and Khare, S., On horizontal and complete lifts of (1; 1) tensor fields F satisfying the structure equation F(2K + S; S) = 0. International Journal of Mathematics and Soft Computing 6 (2016), no. 1, 143-152 . [23] Soylu, Y., A Myers-type compactness theorem by the use of Bakry-Emery Ricci tensor. Differ. Geom. Appl. 54 (2017), 245–250. [24] Soylu, Y., A compactness theorem in Riemannian manifolds. J. Geom. 109 (2018) no. 1, Art. 20, 6 pp.
  • [25] Yano, K. and Patterson, E. M., Horizontal lifts from a manifold to its cotangent bundle. J. Math. Soc. Japan 19 (1967), 185-198. [26] Yano, K. and Ishihara, S., Tangent and Cotangent Bundles. Marcel Dekker Inc., New York, 1973.

On the Lifts of F(2K + S; S)-Structure Satisfying F^(2K+S) + F^S = 0; (F≠ 0; K≥ 0 ,S≥1 ) on Cotangent and Tangent Bundle

Year 2019, Volume: 12 Issue: 1, 71 - 84, 27.03.2019

Haşim Çayır , Fıdan Jabrailzade

https://doi.org/10.36890/iejg.545763
Cited By: 1

Abstract

This paper consists of two main sections. In the first part, we find the integrability conditions by calculating Nijenhuis tensors of the horizontal lifts of F(2K + S, S)−structure Satisfying F 2K+S + F S = 0. Later, we get the results of Tachibana operators applied to vector and covector fields according to the horizontal lifts of F(2K + S, S)−structure in cotangent bundle T ∗ (Mn). Finally,
we have studied the purity conditions of Sasakian metric with respect to the horizontal lifts of the structure. In the second part, all results obtained in the first section were obtained according to the complete and horizontal lifts of F(2K + S, S)−structure in tangent bundle T(Mn). 

Keywords

Integrability conditions Tachibana operators lifts Sasakian metric tangent bundle cotangent bundle

References

  • [1] Akyol, M. A. and Gündüzalp, Y., Hemi-Slant Submersions from Almost Product Riemannian Manifolds. Gulf Journal of Mathematics 4 (2016), no. 3, 15-27.
  • [2] Akyol, M. A. and Gündüzalp, Y., Hemi-Invariant Semi-Riemannian Submersions. Commun. Fac. Sci. Univ. Ank. Series A1 67 (2018), no. 1, 80-92.
  • [3] Andreou, F. G., On integrability conditions of a structure f satisfying f5 + f = 0. Tensor, N.S. 40 (1983), 27-31.
  • [4] Cengiz, N. and Salimov, A. A., Diagonal Lift in the Tensor Bundle and its Applications. Applied Mathematics and Computation 142 (2003) 309-319.
  • [5] Çayır, H., Some Notes on Lifts of Almost Paracontact Structures. American Review of Mathematics and Statistics 3 (2015), no. 1, 52-60.
  • [6] Çayır, H., Lie derivatives of almost contact structure and almost paracontact structure with respect to XV and XH on tangent bundle T(M). Proceedings of the Institute of Mathematics and Mechanics 42 (2016), no. 1, 38-49.
  • [7] Çayır, H., Tachibana and Vishnevskii Operators Applied to XV and XH in Almost Paracontact Structure on Tangent Bundle T(M). New Trends in Mathematical Sciences 4 (2016), no. 3, 105-115.
  • [8] Çayır, H. and Köseoğlu, G., Lie Derivatives of Almost Contact Structure and Almost Paracontact Structure With Respect to XC and XV on Tangent Bundle T(M). New Trends in Mathematical Sciences 4 (2016), no. 1, 153-159.
  • [9] Das, L., On CR-structure and an f(2K + 4; 2)-structure satisfying f^(2K+4)+ f^2 = 0. Tensor 73 (2011), no. 3, 222-227.
  • [10] Das, L., On lifts of structure satisfying F^( K+1)− a^2 F^(K−1). Kyungpook Mathematical Journal 40 (2000), no. 2, 391-398.
  • [11] Gupta, V.C., Integrability Conditions of a Structure F Satisfying F^K + F = 0: The Nepali Math. Sc. Report 14 (1998), no. 2, 55-62.
  • [12] Ishıhara, S. and Yano, K., On integrability conditions of a structure f satisfying f^3 + f = 0: Quaterly J. Math. 15 (1964), 217-222.
  • [13] Kobayashi, S. and Nomizu, K., Foundations of Differential Geometry-Volume I. John Wiley & Sons, Inc, New York, 1963.
  • [14] Lovejoy, S. D., Nivas, R. and Pathak, V. N., On horizontal and complete lifts from a manifold with fλ(7; 1)-structure to its cotangent bundle. International Journal of Mathematics and Mathematical Sciences 8 (2005), 1291-1297.
  • [15] Musso, E. and Tricerri, F., Riemannian Metric on Tangent Bundles. Ann. Math. Pura. Appl. 150 (1988), no. 4, 1-9.
  • [16] Nivas, R. and Prasad, C. S., On a structure defined by a tensor field f(≠ 0) of type (1; 1) satisfying f^5 - a^2 f = 0. Nep. Math. Sc. Rep. 10 (1985), no. 1, 25-30.
  • [17] Sahin, B.,Anti-invariant Riemannian submersions from almost Hermitian manifolds. CentralEuropean J.Math. 3 (2010), 437-447.
  • [18] Sahin, B., Semi-invariant Riemannian submersions from almost Hermitian manifolds. Canad.Math. Bull. 56 (2013), 173-183.
  • [19] Salimov, A. A., Tensor Operators and Their applications. Nova Science Publ., New York, 2013.
  • [20] Salimov, A. A. and Çayır, H., Some Notes On Almost Paracontact Structures. C. R. Acad. Bulgare Sci. 66 (2013), no. 3, 331-338.
  • [21] Singh, A., On CR􀀀structures F􀀀structures satisfying F^(2K+P) + F^P = 0. Int. J. Contemp. Math. Sciences 4 (2009), 1029-1035.
  • [22] Singh, A., Pandey, R. K. and Khare, S., On horizontal and complete lifts of (1; 1) tensor fields F satisfying the structure equation F(2K + S; S) = 0. International Journal of Mathematics and Soft Computing 6 (2016), no. 1, 143-152 . [23] Soylu, Y., A Myers-type compactness theorem by the use of Bakry-Emery Ricci tensor. Differ. Geom. Appl. 54 (2017), 245–250. [24] Soylu, Y., A compactness theorem in Riemannian manifolds. J. Geom. 109 (2018) no. 1, Art. 20, 6 pp.
  • [25] Yano, K. and Patterson, E. M., Horizontal lifts from a manifold to its cotangent bundle. J. Math. Soc. Japan 19 (1967), 185-198. [26] Yano, K. and Ishihara, S., Tangent and Cotangent Bundles. Marcel Dekker Inc., New York, 1973.
There are 23 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Haşim Çayır

Fıdan Jabrailzade This is me

Publication Date March 27, 2019
Published in Issue Year 2019 Volume: 12 Issue: 1

Cite

APA Çayır, H., & Jabrailzade, F. (2019). On the Lifts of F(2K + S; S)-Structure Satisfying F^(2K+S) + F^S = 0; (F≠ 0; K≥ 0 ,S≥1 ) on Cotangent and Tangent Bundle. International Electronic Journal of Geometry, 12(1), 71-84. https://doi.org/10.36890/iejg.545763
AMA Çayır H, Jabrailzade F. On the Lifts of F(2K + S; S)-Structure Satisfying F^(2K+S) + F^S = 0; (F≠ 0; K≥ 0 ,S≥1 ) on Cotangent and Tangent Bundle. Int. Electron. J. Geom. March 2019;12(1):71-84. doi:10.36890/iejg.545763
Chicago Çayır, Haşim, and Fıdan Jabrailzade. “On the Lifts of F(2K + S; S)-Structure Satisfying F^(2K+S) + F^S = 0; (F≠ 0; K≥ ,S≥1 ) on Cotangent and Tangent Bundle”. International Electronic Journal of Geometry 12, no. 1 (March 2019): 71-84. https://doi.org/10.36890/iejg.545763.
EndNote Çayır H, Jabrailzade F (March 1, 2019) On the Lifts of F(2K + S; S)-Structure Satisfying F^(2K+S) + F^S = 0; (F≠ 0; K≥ 0 ,S≥1 ) on Cotangent and Tangent Bundle. International Electronic Journal of Geometry 12 1 71–84.
IEEE H. Çayır and F. Jabrailzade, “On the Lifts of F(2K + S; S)-Structure Satisfying F^(2K+S) + F^S = 0; (F≠ 0; K≥ 0 ,S≥1 ) on Cotangent and Tangent Bundle”, Int. Electron. J. Geom., vol. 12, no. 1, pp. 71–84, 2019, doi: 10.36890/iejg.545763.
ISNAD Çayır, Haşim - Jabrailzade, Fıdan. “On the Lifts of F(2K + S; S)-Structure Satisfying F^(2K+S) + F^S = 0; (F≠ 0; K≥ ,S≥1 ) on Cotangent and Tangent Bundle”. International Electronic Journal of Geometry 12/1 (March 2019), 71-84. https://doi.org/10.36890/iejg.545763.
JAMA Çayır H, Jabrailzade F. On the Lifts of F(2K + S; S)-Structure Satisfying F^(2K+S) + F^S = 0; (F≠ 0; K≥ 0 ,S≥1 ) on Cotangent and Tangent Bundle. Int. Electron. J. Geom. 2019;12:71–84.
MLA Çayır, Haşim and Fıdan Jabrailzade. “On the Lifts of F(2K + S; S)-Structure Satisfying F^(2K+S) + F^S = 0; (F≠ 0; K≥ ,S≥1 ) on Cotangent and Tangent Bundle”. International Electronic Journal of Geometry, vol. 12, no. 1, 2019, pp. 71-84, doi:10.36890/iejg.545763.
Vancouver Çayır H, Jabrailzade F. On the Lifts of F(2K + S; S)-Structure Satisfying F^(2K+S) + F^S = 0; (F≠ 0; K≥ 0 ,S≥1 ) on Cotangent and Tangent Bundle. Int. Electron. J. Geom. 2019;12(1):71-84.

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