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Adel Mohammed Ali Al Qashbari Aminah Omar Awadh Mubark

Abstract

In this paper, we investigate the decomposition of Cartan's third curvature tensor  in the framework of generalized -nth recurrent Finsler spaces. We examine three distinct decompositions of the curvature tensor and analyze the resulting equations under covariant derivatives of the decomposed tensor fields. The decompositions are expressed in terms of independent tensor fields, and we explore the recurrence properties of the resulting decomposition tensors. We show that under certain conditions, these decomposition tensors exhibit generalized nth-recurrence properties, which are crucial for understanding the geometric behavior of these tensors in Finsler geometry. The results provide a deeper understanding of the curvature properties in higher-dimensional recurrent Finsler spaces, with implications for both theoretical and applied geometry.

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Keywords

Finsler manifold, generalized recurrent tensor field, decomposition

Section
Articles
How to Cite
Al Qashbari, A. M. A., & Mubark, A. O. A. (2025). Decomposition of Generalized Recurrent Tensor Fields of R^h-nth Order in Finsler Manifolds. Journal of Science and Technology, 30(2). https://doi.org/10.20428/jst.v30i2.2664