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

Haşim Çayır; Behboudi Asl

doi:10.36890/iejg.1170443

Research Article

Year 2023, , 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, , 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

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 (April 2023), 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.