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Interrelations Among Concircular, Conformal and Conharmonic Curvatures in Fifth-Order Recurrent Finsler Spaces

Year: 2025
Type: article
Abstract: The significance of this research lies in the generalization of curvature tensors, particularly the concircular curvature tensor, which is studied as a fifth recurrent tensor within the framework of Cartan’s fourth curvature tensor. It contributes to the fundamental understanding of geometric properties in Finsler spaces. This paper builds upon new the concircular curvature tensor π‘€π‘–π‘—π‘˜β„Ž in generaralized fifth recurrent Finsler space that Cartan's fourth curvature tensor πΎπ‘—π‘˜β„Ž 𝑖 in sense of Berwald (𝐺ℬ𝐾 βˆ’ 5𝑅𝐹𝑛) via Lie derivative. We obtain the relation between the concircular curvature tensor π‘€π‘–π‘—π‘˜β„Ž , conformal curvature tensor πΆπ‘–π‘—π‘˜β„Ž , conharmonic curvature tensor πΏπ‘–π‘˜β„Ž π‘Ÿ and associate curvature tensor π‘…π‘–π‘—π‘˜β„Ž if the metric tensor π‘”π‘Ÿπ‘— = 1 by Lie - derivative. Also, we show these curvature tensors have the same extension and direction. In addition, the concircular curvature tensor and conharmonic curvature tensor πΏπ‘—π‘˜β„Ž 𝑖 are co-directional. We prove that the concircular curvature tensor π‘€π‘–π‘—π‘˜β„Ž behaves as fifth recurrent by Lie derivative in the main space.
DOI: 10.37394/23206.2025.24.80
Language: English
Open Access status: diamond
OpenAlex ID: W7163554698
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Cites: 8
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Related to: 10