Berwald and Chern Connections under Anisotropic Conformal Transformations on Conic Pseudo-Finsler Surfaces

Kotb, Ali Abd-Elghany; Elgendi, Salah Ahmed; Taha, Ebtsam Hassan; Youssef, Nabil Labib; Trabia, Ahmed

doi:10.21608/sjdfs.2025.402824.1246

Berwald and Chern Connections under Anisotropic Conformal Transformations on Conic Pseudo-Finsler Surfaces

Document Type : Original articles

Authors

¹ Department of mathematics,Faculty of Science, Damietta University New Damietta, Egypt

² Department of Mathematics, faculty of science, Benha university

³ Department of mathematics, faculty of science, Cairo university

⁴ Department of Mathematics, Faculty of Science, Cairo University, Giza, Egyp

⁵ mathematics Damietta university

10.21608/sjdfs.2025.402824.1246

Abstract

This paper builds upon our previous work on the anisotropic conformal change F(x,y)↦¯F(x,y)=e^(ϕ(x,y)) F(x,y). The primary aim of this study is to investigate the behavior of the Berwald connection, which quantifies how far a Finsler structure deviates from Riemannian one, and the Chern-Rund connection on conic pseudo-Finsler surfaces under this anisotropic conformal transformation, along with the dynamical covariant derivative. In particular, we derive the Landsberg tensor of the transformed Finsler metric ¯F by expressing it in terms of the difference between the horizontal coefficients of the Berwald and Chern-Rund connections. Consequently, we find the necessary and sufficient conditions under which the Landsbergian property is preserved under the anisotropic conformal transformation. This approach provides new insight into the interplay between anisotropic conformal transformation and the intrinsic geometry of Finsler surfaces. Furthermore, we obtain explicit expressions for the anisotropic conformal transformation of the dynamical covariant derivatives in the context of conic pseudo-Finsler surfaces.

Keywords