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Year 2023, Volume: 16 Issue: 1, 104 - 110, 30.04.2023

Haşim Çayır , Behboudi Asl

https://doi.org/10.36890/iejg.1170443

Abstract

References

  • [1] N. Cengiz and A. A. Salimov, Complete lifts of derivations to tensor bundles, Bol. Soc. Mat. Mexicana (3) 8 (2002), no. 1, 75--82.
  • [2] H.Çayır, Tachibana and Vishnevskii Operators Applied to $X^{V}$ and $X^{C}$ in Almost Paracontact Structure on Tangent Bundle T(M), Ordu Üniversitesi Bilim ve Teknoloji Dergisi, Ordu Üniversitesi, 6 (1) (2016) 67-82.
  • [3] H.Çayır, Tachibana and Vishnevskii Operators Applied to $X^{V}$ and $X^{C}$ in Almost Paracontact Structure on Tangent Bundle T(M), New Trends in Mathematical Sciences, 4 (3) (2016) 105-115.
  • [4] A. Gezer and A.A. Salimov, Diagonal lifts of tensor fields of type (1,1) on cross-sections in tensor bundles and ıts applications, J. Korean Math. Soc. 45(2008), no.2, 367-376.
  • [5] A. Ledger and K. Yano, Almost complex structures on tensor bundles, J. Differential Geometry 1 (1967), 355--368.
  • [6] A. Mağden, N. Cengiz, and A. A. Salimov, Horizontal lift of affinor structures and its applications, Appl. Math. Comput. 156 (2004), no. 2, 455--461.
  • [7] A. Mağden and A. A. Salimov, Horizontal lifts of tensor fields to sections of the tangent bundle, Izv. Vyssh. Uchebn. Zaved. Mat. (2001), no. 3, 77--80; translation in Russian Math. (Iz. VUZ) 45 (2001), no. 3, 73-76.
  • [8] A. A. Salimov, A new method in the theory of liftings of tensor fields in a tensor bundle, Izv. Vyssh. Uchebn. Zaved. Mat. (1994), no. 3, 69--75; translation in Russian Math. (Iz. VUZ) 38 (1994), no. 3, 67-73.
  • [9] A.A.Salimov, Tensor Operators and Their applications, Nova Science Publ., New York (2013).
  • [10] A.A.Salimov, H.Çayır, Some Notes On Almost Paracontact Structures, Comptes Rendus de 1'Acedemie Bulgare Des Sciences, 66 (3) (2013) 331-338.
  • [11] A. A. Salimov, A. Gezer and K. Akbulut, Geodesics of Sasakian metrics on tensor bundles, Mediterranean Journal of Mathematics, 6 (2009). 135-147.
  • [12] K. Yano and S. Ishihara, Tangent and Cotangent Bundles: Differential Geometry, Pure and Applied Mathematics, No. 16. Marcel Dekker, Inc., New York, 1973.
  • [13] K. Yano and M. Kon, Structures on Manifolds, Series in Pure Mathematics, 3. World Scientific Publishing Co., Singapore, 1984.

Operators Applied to Lifts with Respect to the Diagonal Lifts of Affinor Fields Along a Cross-Section on $T_{q}^{p}(M)$

Year 2023, Volume: 16 Issue: 1, 104 - 110, 30.04.2023

Haşim Çayır , Behboudi Asl

https://doi.org/10.36890/iejg.1170443

Abstract

In this paper firstly, operators were applied to vertical and horizontal lifts with respect to the diagonal lift $ϕ^{D}$ of tensor fields of type (1,1) from manifold to its tensor bundle of type (p,q) along the cross-section, respectively. Secondly, we get the conditions of almost holomorfic vector field with respect to $ϕ^{D}$ on $T_{q}^{p}(M)$.

Keywords

Cross-section Tachibana operators Vishnevskii operators diagonal lift horizontal lift vertical lift

References

  • [1] N. Cengiz and A. A. Salimov, Complete lifts of derivations to tensor bundles, Bol. Soc. Mat. Mexicana (3) 8 (2002), no. 1, 75--82.
  • [2] H.Çayır, Tachibana and Vishnevskii Operators Applied to $X^{V}$ and $X^{C}$ in Almost Paracontact Structure on Tangent Bundle T(M), Ordu Üniversitesi Bilim ve Teknoloji Dergisi, Ordu Üniversitesi, 6 (1) (2016) 67-82.
  • [3] H.Çayır, Tachibana and Vishnevskii Operators Applied to $X^{V}$ and $X^{C}$ in Almost Paracontact Structure on Tangent Bundle T(M), New Trends in Mathematical Sciences, 4 (3) (2016) 105-115.
  • [4] A. Gezer and A.A. Salimov, Diagonal lifts of tensor fields of type (1,1) on cross-sections in tensor bundles and ıts applications, J. Korean Math. Soc. 45(2008), no.2, 367-376.
  • [5] A. Ledger and K. Yano, Almost complex structures on tensor bundles, J. Differential Geometry 1 (1967), 355--368.
  • [6] A. Mağden, N. Cengiz, and A. A. Salimov, Horizontal lift of affinor structures and its applications, Appl. Math. Comput. 156 (2004), no. 2, 455--461.
  • [7] A. Mağden and A. A. Salimov, Horizontal lifts of tensor fields to sections of the tangent bundle, Izv. Vyssh. Uchebn. Zaved. Mat. (2001), no. 3, 77--80; translation in Russian Math. (Iz. VUZ) 45 (2001), no. 3, 73-76.
  • [8] A. A. Salimov, A new method in the theory of liftings of tensor fields in a tensor bundle, Izv. Vyssh. Uchebn. Zaved. Mat. (1994), no. 3, 69--75; translation in Russian Math. (Iz. VUZ) 38 (1994), no. 3, 67-73.
  • [9] A.A.Salimov, Tensor Operators and Their applications, Nova Science Publ., New York (2013).
  • [10] A.A.Salimov, H.Çayır, Some Notes On Almost Paracontact Structures, Comptes Rendus de 1'Acedemie Bulgare Des Sciences, 66 (3) (2013) 331-338.
  • [11] A. A. Salimov, A. Gezer and K. Akbulut, Geodesics of Sasakian metrics on tensor bundles, Mediterranean Journal of Mathematics, 6 (2009). 135-147.
  • [12] K. Yano and S. Ishihara, Tangent and Cotangent Bundles: Differential Geometry, Pure and Applied Mathematics, No. 16. Marcel Dekker, Inc., New York, 1973.
  • [13] K. Yano and M. Kon, Structures on Manifolds, Series in Pure Mathematics, 3. World Scientific Publishing Co., Singapore, 1984.
There are 13 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Haşim Çayır 0000-0003-0348-8665

Behboudi Asl 0000-0003-1682-1391

Publication Date April 30, 2023
Acceptance Date September 18, 2022
Published in Issue Year 2023 Volume: 16 Issue: 1

Cite

APA Çayır, H., & Asl, B. (2023). Operators Applied to Lifts with Respect to the Diagonal Lifts of Affinor Fields Along a Cross-Section on $T_{q}^{p}(M)$. International Electronic Journal of Geometry, 16(1), 104-110. https://doi.org/10.36890/iejg.1170443
AMA Çayır H, Asl B. Operators Applied to Lifts with Respect to the Diagonal Lifts of Affinor Fields Along a Cross-Section on $T_{q}^{p}(M)$. Int. Electron. J. Geom. April 2023;16(1):104-110. doi:10.36890/iejg.1170443
Chicago Çayır, Haşim, and Behboudi Asl. “Operators Applied to Lifts With Respect to the Diagonal Lifts of Affinor Fields Along a Cross-Section on $T_{q}^{p}(M)$”. International Electronic Journal of Geometry 16, no. 1 (April 2023): 104-10. https://doi.org/10.36890/iejg.1170443.
EndNote Çayır H, Asl B (April 1, 2023) Operators Applied to Lifts with Respect to the Diagonal Lifts of Affinor Fields Along a Cross-Section on $T_{q}^{p}(M)$. International Electronic Journal of Geometry 16 1 104–110.
IEEE H. Çayır and B. Asl, “Operators Applied to Lifts with Respect to the Diagonal Lifts of Affinor Fields Along a Cross-Section on $T_{q}^{p}(M)$”, Int. Electron. J. Geom., vol. 16, no. 1, pp. 104–110, 2023, doi: 10.36890/iejg.1170443.
ISNAD Çayır, Haşim - Asl, Behboudi. “Operators Applied to Lifts With Respect to the Diagonal Lifts of Affinor Fields Along a Cross-Section on $T_{q}^{p}(M)$”. International Electronic Journal of Geometry 16/1 (April2023), 104-110. https://doi.org/10.36890/iejg.1170443.
JAMA Çayır H, Asl B. Operators Applied to Lifts with Respect to the Diagonal Lifts of Affinor Fields Along a Cross-Section on $T_{q}^{p}(M)$. Int. Electron. J. Geom. 2023;16:104–110.
MLA Çayır, Haşim and Behboudi Asl. “Operators Applied to Lifts With Respect to the Diagonal Lifts of Affinor Fields Along a Cross-Section on $T_{q}^{p}(M)$”. International Electronic Journal of Geometry, vol. 16, no. 1, 2023, pp. 104-10, doi:10.36890/iejg.1170443.
Vancouver Çayır H, Asl B. Operators Applied to Lifts with Respect to the Diagonal Lifts of Affinor Fields Along a Cross-Section on $T_{q}^{p}(M)$. Int. Electron. J. Geom. 2023;16(1):104-10.
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