University of Mohaghegh Ardabili Journal of Finsler Geometry and its Applications 2783-0500 7 1 2026 05 01 Adapted connections on foliated manifolds 94 102 4236 10.22098/jfga.2025.17686.1165 EN Zohreh Nazari Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran Elham Zangiabadi Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran Journal Article 2025 06 21 ‎In this study‎, ‎we define the local components of the adapted connection relative to the adapted frame field‎. ‎We also calculate the covariant derivative of a tensor with respect to this connection‎. ‎Furthermore‎, ‎we present a classification of totally geodesic foliations and bundle-like metrics‎, ‎along with the introduction of the local components of the torsion tensor associated with this connection‎. ‎To illustrate our findings‎, ‎we provide a relevant example‎. https://jfga.uma.ac.ir/article_4236_7c891d8137ec04eb79a420e1a6e3ff91.pdf