Fourth-Order P^h-Recurrent Structures in Affinely Connected Finsler Spaces with Perspectives on Nonlinear Stability

Abstract

In the context of affinely connected Finsler spaces, the theoretical underpinnings of higher-order recurrent geometric forms are examined in this research. With a particular focus on Cartan's second curvature tensor , we examine the necessary and sufficient conditions for the existence of generalized -four-recurrent spaces. Several theorems governing the behavior of linked curvature and torsion tensors are derived by using the -covariant derivative of the fourth order. In addition to the mathematical derivation, the article talks about how these higher-order structures can be used in nonlinear stability analysis. The "curvature" and "recurrence" characteristics of these spaces, where non-linear fluctuations and systemic persistence are common, offer a strong mathematical analogy for simulating the dynamics of fintech-driven financial stability and the course of economic recovery.

This paper establishes a mathematical analogy between the directional curvature of Finsler manifolds and the non-linear fluctuations in fintech-driven financial systems