This paper investigates novel transformations of affine connections and the derivation of their corresponding invariants within the framework of differential geometry. Drawing inspiration from previously established (m¯,m)-conformal mappings, we introduce a generalized class of these transformations. We successfully derive three fundamental invariants for this class. To demonstrate the geometric significance of these structures, we examine their implications within the calculus of variations. Finally, we provide potential physical interpretations of the obtained results, suggesting their relevance in theoretical physics.
