Advanced techniques for decomposing recurrent curvature tensors in Tachibana spaces and generalized geometric structures

Abstract

This paper presents a comprehensive analysis of advanced techniques for decomposing recurrent curvature tensors across diverse geometric frameworks. By integrating classical methodologies with modern approaches, we develop novel methods that enhance the understanding of recurrent tensors within complex geometric settings. Our study extends the mathematical foundations of tensor decomposition with a focus on its implications for Kählerian and Tachibana structures. Through rigorous theoretical analysis and computational simulations, we demonstrate the efficacy of these methods, offering precise and meaningful results. This investigation specifically addresses the recurrent and bi-recurrent behaviors of curvature tensor fields in these spaces, providing new insights into their geometric structures. We also explore the implications of the Bianchi identity and introduce the concept of Weyl-concircular curvature tensor field and tri-recurrent Tachibana spaces. A detailed analysis of the decomposition of curvature tensors and covariant tensor fields is presented, utilizing advanced mathematical tools and techniques.