On the Covariant Structure and Decomposition of Weyl's Projective Curvature Tensor in Generalized Recurrent Finsler Geometry

Adel Mohammed Ali Al-qashbari; Abhıjıt Mandal; Fahmi Assallal; Mustafa Yıldırım

doi:10.47000/tjmcs.1740350

On the Covariant Structure and Decomposition of Weyl's Projective Curvature Tensor in Generalized Recurrent Finsler Geometry

Abstract

In this work, we introduce and investigate two new classes of Finsler spaces: generalized $W^{\ }_{|h}${}-recurrent spaces and generalized $W^{\ }_{|h}${}-birecurrent spaces, which extend classical notions of recurrence and birecurrence to a broader geometric setting. These spaces are defined via specific covariant derivative conditions imposed on Weyl's projective curvature tensor $W^i_{jkh}${}, involving scalar functions ${\lambda }_m$,$\ {\mu }_m$, and ${\gamma }_m${}. We establish several structural identities characterizing the recurrence properties of these tensors and examine higher-order covariant derivatives. Additionally, we explore the decomposition of the curvature tensor $W^i_{jkh}$ in terms of lower-rank tensors, considering cases where the tensor is expressed as a product of a covariant vector and a mixed-type tensor. The recurrence and birecurrence properties of such decompositions are studied under various tensorial conditions. Our analysis shows that under appropriate assumptions on the covariant vector and tensor fields, the decomposed tensors inherit generalized birecurrence properties, and remain non-vanishing, emphasizing the consistency of the new structure with existing geometric frameworks. Here, $a_{ml}={\lambda }_{m|l}+{\lambda }_m{\lambda }_{l\ }$, $\ b_{ml}={\text{\^{A} $\mu$ }}_{m|l}+{\lambda }_m{\text{\^{A} $\mu$% }}_l$ and $c_{ml}={({\lambda }_m{\gamma }_l+\gamma }_{m|l})$ are non-zero covariant tensors field of second order, respectively.

Keywords

References

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Details

Primary Language

English

Subjects

Algebraic and Differential Geometry

Journal Section

Research Article

Authors

Adel Mohammed Ali Al-qashbari
0000-0002-0556-9293
Yemen

Abhıjıt Mandal ^*
0000-0002-3979-8916
India

Fahmi Assallal
0000-0000-0000-0000
Yemen

Mustafa Yıldırım
0000-0002-7805-1492
Türkiye

Publication Date

October 13, 2026

Submission Date

July 11, 2025

Acceptance Date

April 24, 2026

Published in Issue

Year 2026 Volume: 18 Number: 3

DOI

https://doi.org/10.47000/tjmcs.1740350

IZ

https://izlik.org/JA89YW88HH

Cite

RIS / Bibtex

APA

Al-qashbari, A. M. A., Mandal, A., Assallal, F., & Yıldırım, M. (2026). On the Covariant Structure and Decomposition of Weyl’s Projective Curvature Tensor in Generalized Recurrent Finsler Geometry. Turkish Journal of Mathematics and Computer Science, 18(3), 863-876. https://doi.org/10.47000/tjmcs.1740350

AMA

1.Al-qashbari AMA, Mandal A, Assallal F, Yıldırım M. On the Covariant Structure and Decomposition of Weyl’s Projective Curvature Tensor in Generalized Recurrent Finsler Geometry. TJMCS. 2026;18(3):863-876. doi:10.47000/tjmcs.1740350

Chicago

Al-qashbari, Adel Mohammed Ali, Abhıjıt Mandal, Fahmi Assallal, and Mustafa Yıldırım. 2026. “On the Covariant Structure and Decomposition of Weyl’s Projective Curvature Tensor in Generalized Recurrent Finsler Geometry”. Turkish Journal of Mathematics and Computer Science 18 (3): 863-76. https://doi.org/10.47000/tjmcs.1740350.

EndNote

Al-qashbari AMA, Mandal A, Assallal F, Yıldırım M (October 1, 2026) On the Covariant Structure and Decomposition of Weyl’s Projective Curvature Tensor in Generalized Recurrent Finsler Geometry. Turkish Journal of Mathematics and Computer Science 18 3 863–876.

IEEE

[1]A. M. A. Al-qashbari, A. Mandal, F. Assallal, and M. Yıldırım, “On the Covariant Structure and Decomposition of Weyl’s Projective Curvature Tensor in Generalized Recurrent Finsler Geometry”, TJMCS, vol. 18, no. 3, pp. 863–876, Oct. 2026, doi: 10.47000/tjmcs.1740350.

ISNAD

Al-qashbari, Adel Mohammed Ali - Mandal, Abhıjıt - Assallal, Fahmi - Yıldırım, Mustafa. “On the Covariant Structure and Decomposition of Weyl’s Projective Curvature Tensor in Generalized Recurrent Finsler Geometry”. Turkish Journal of Mathematics and Computer Science 18/3 (October 1, 2026): 863-876. https://doi.org/10.47000/tjmcs.1740350.

JAMA

1.Al-qashbari AMA, Mandal A, Assallal F, Yıldırım M. On the Covariant Structure and Decomposition of Weyl’s Projective Curvature Tensor in Generalized Recurrent Finsler Geometry. TJMCS. 2026;18:863–876.

MLA

Al-qashbari, Adel Mohammed Ali, et al. “On the Covariant Structure and Decomposition of Weyl’s Projective Curvature Tensor in Generalized Recurrent Finsler Geometry”. Turkish Journal of Mathematics and Computer Science, vol. 18, no. 3, Oct. 2026, pp. 863-76, doi:10.47000/tjmcs.1740350.

Vancouver

1.Adel Mohammed Ali Al-qashbari, Abhıjıt Mandal, Fahmi Assallal, Mustafa Yıldırım. On the Covariant Structure and Decomposition of Weyl’s Projective Curvature Tensor in Generalized Recurrent Finsler Geometry. TJMCS. 2026 Oct. 1;18(3):863-76. doi:10.47000/tjmcs.1740350