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Decomposition and Generalized Recurrence of Cartan’s Third Curvature Tensor in Generalized -Recurrent Finsler Spaces

Year: 2026

Type: article

Abstract: This paper investigates the decomposition properties of Cartan’s third curvature tensor in generalized recurrent Finsler spaces. More precisely, we consider an -dimensional Finsler space equipped with Cartan’s connection and satisfying a generalized recurrence condition for the third curvature tensor. Several decomposable forms of the curvature tensor are examined, including , , and . By applying -covariant differentiation, tensor contraction, and transvection with respect to the supporting element , we derive recurrence relations for the corresponding decomposition tensors. Under suitable constancy and covariant-constancy assumptions on the associated tensor fields, we establish that the resulting decomposed curvature tensors inherit generalized recurrence properties. Further consequences are obtained for the contracted tensors , , and . The obtained results provide a systematic characterization of decomposable Cartan curvature tensors and their recurrence behavior, thereby extending the structural analysis of recurrent curvature tensors in Finsler geometry.

Source: Journal of Science and Technology

DOI: 10.20428/jst.v31i9.4227

Authors: Al-Qashbari , Adel Mohammed Ali, Hanbala, Amani M. A., Irhouma, Mukhtar Abdulsalam

Institutions: University of Science and Technology, Wadi Alshatti University

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W7225629385

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