Higher-Order Recurrence in Tachibana Spaces and Curvature Compatibility with Weyl-Tachibana and H-Concircular Structures
DOI:
https://doi.org/10.69980/ajpr.v28i4.277Keywords:
Tachibana space, r-recurrence, recurrent curvature tensor, Weyl-Tachibana tensor, H-concircular tensorAbstract
This study explores the geometric structure of Tachibana spaces equipped with higher-order recurrent curvature tensors. Building upon foundational concepts in almost Hermitian and Kahlerian geometry, we define and investigate r-recurrent Tachibana spaces (r -spaces) and analyze the associated recurrence conditions in Weyl-Tachibana and Tachibana H-concircular curvature tensors, denoted respectively as Z-r and E-r spaces. We establish necessary and sufficient conditions under which these recurrence structures are mutually equivalent or imply one another. Furthermore, the study reveals the interdependence between recurrence in various curvature tensors, contributing to a more unified understanding of higher-order geometric structures. The findings extend classical results in Kahlerian geometry and provide potential applications in differential geometry, mathematical physics, and symmetric theoretical models.
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