Computational Extensions of Generalized -Recurrent Finsler Spaces and Applications to Geometric Machine Learning

Abstract

We investigate generalized -recurrent Finsler spaces defined via a recurrence condition on Cartan’s third curvature tensor. We derive identities involving Cartan torsion, Berwald torsion , the deviation tensor , and Ricci-type contractions. In particular, we prove non-degeneracy results showing that the Ricci tensor, curvature vector, deviation tensor, and scalar curvature are necessarily non-vanishing. We also provide equivalent characterizations of generalized -recurrence through contracted forms of the defining condition. Finally, we outline how these identities can support curvature-aware numerical schemes for manifold optimization and geometric machine learning in anisotropic settings.