A New Transformation Rule Between Finsler Metrics and Its Geometric Implications on Tangent Structures and Conformal Invariants

Abstract

This paper introduces a new transformation rule between Finsler metrics and investigates its geometric implications within the framework of conformal Finsler geometry. Finsler geometry extends Riemannian geometry by allowing metric dependence on both positional and directional variables, providing a suitable setting for studying anisotropic structures. The proposed transformation is derived from existing conformal relations and is formulated to establish new connections between different Finsler spaces. The behavior of tangent vectors, dual vectors, unit vectors, and associated geometric quantities under the transformation is analyzed. Explicit transformation formulas are obtained, and several fundamental identities are established. Theoretical results are derived to describe the invariance and structural properties of the transformed geometric objects. The proposed framework generalizes aspects of classical conformal transformations and provides a broader perspective for studying metric relations in Finsler geometry. These findings contribute to the development of transformation theory in Finsler spaces and may support future investigations involving geometric invariants, curvature structures, and applications in differential geometry and mathematical physics.