Characterization and Transformation of Affine and Homothetic Motions in the Framework of Fifth‐Order Recurrent Finsler Manifolds
Adel M. Al-Qashbari, S. Saleh, Alaa M. Abd El-latif, Saeedah M. Baleedi, M. I. Elashiry, Mohamed Said Mohamed, Khaled A. Aldwoah, Hanan H. Sakr
Source abstract
The study of affine and homothetic motions in Finsler geometry plays a crucial role in understanding the intrinsic symmetries of geometric structures. In particular, recurrent Finsler spaces provide a rich framework for analyzing higher‐order geometric properties. Despite significant developments in lower‐order recurrent structures, the investigation of fifth‐order recurrence remains relatively unexplored. This motivates the present study, where we aim to characterize such motions and establish conditions for their transformations. In this paper, we introduce specific types of affine and homothetic motions in a generalized ‐fifth recurrent Finsler space. Our aim is to derive various identities representing these motions on via Lie derivatives. We obtain certain conditions for transforming homothetic motions into affine motions.
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