University of Mohaghegh Ardabili Journal of Finsler Geometry and its Applications 2783-0500 7 1 2026 05 01 Intrinsic Holmes-Thompson volumes and rigidity in Weil bundles 1 19 4154 10.22098/jfga.2025.17576.1161 EN Tchuiaga Stephane Department of Mathematics, University of Buea, South West Region, Cameroon Journal Article 2025 05 31 This paper develops a framework for defining intrinsic volumes on manifolds M by leveraging the structure of Weil bundles M^A associated with Weil algebras A. We explore constructions for a Finsler-like structure F_A primarily on the fibers of M^A, aiming to derive it from the algebraic properties of A with minimal reliance on auxiliary metrics on M. The concept of A-naturality is introduced to formalize the intrinsic nature of such structures. From this fiberwise F_A, an effective Finsler structure F_M on the tangent bundle TM is derived. The Busemann-Hausdorff measure dV_F associated with F_Mthen provides a volume form on M. We establish foundational results concerning conditions under which a diffeomorphism ø: M → M preserves dV_F, linking this to the behavior of its prolongation ø^A and exploring resulting rigidity phenomena, including a characterization theorem for dV_F under affine symmetries. Furthermore, we propose several significant conjectures and future research directions concerning infinitesimal symmetries, axiomatic uniqueness of these volumes, interactions with curvature, sub-Riemannian limits, and holonomy restrictions. https://jfga.uma.ac.ir/article_4154_465d319702b0e7d95d6a512cea024104.pdf