IIARD International Institute of Academic Research and Development

INTERNATIONAL JOURNAL OF APPLIED SCIENCES AND MATHEMATICAL THEORY (IJASMT )

E- ISSN 2489-009X
P- ISSN 2695-1908
VOL. 11 NO. 1 2025
DOI: 10.56201/ijasmt.vol.11.no1.2025.pg1.9

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A Study of M-Projective Curvature Tensor in Via Lie Derivative

Adel M. Al-Qashbari, Alaa A. Abdallah & Saeedah M. Baleedi

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Abstract

In this paper, we investigate the M-projective curvature tensor ?? ??? ? in generalized fifth recurrence Finsler space for Cartan's fourth curvature tensor in sense of Berwald by using ???-derivative. Our study aims to provide new insights into the geometric properties of these spaces and the behavior of the M-projective curvature tensor ?? ??? ? under Lie differentiation. By employing the Lie derivative, we are able to derive new identities and relations involving the M-projective curvature tensor ?? ??? ? . We get relationships between some tensors when the M-projective curvature tensor ?? ??? ? is collineation along a vector field ? ? (?). Furthermore, we obtain the Berwald covariant derivative of fifth order for some tensors are vanishing and we establish various identities on ???-derivative in ??? ? 5???.

keywords:

M-projective curvature tensor ?? ??? ? , Generalized ?? ?fifth recurrent space, Berwald covariant derivative of fifth order, ???-derivative.

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