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Stephane, Tchuiaga. (1405). Intrinsic Holmes-Thompson volumes and rigidity in Weil bundles. سامانه مدیریت نشریات علمی, 7(1), 1-19. doi: 10.22098/jfga.2025.17576.1161
Tchuiaga Stephane. "Intrinsic Holmes-Thompson volumes and rigidity in Weil bundles". سامانه مدیریت نشریات علمی, 7, 1, 1405, 1-19. doi: 10.22098/jfga.2025.17576.1161
Stephane, Tchuiaga. (1405). 'Intrinsic Holmes-Thompson volumes and rigidity in Weil bundles', سامانه مدیریت نشریات علمی, 7(1), pp. 1-19. doi: 10.22098/jfga.2025.17576.1161
Stephane, Tchuiaga. Intrinsic Holmes-Thompson volumes and rigidity in Weil bundles. سامانه مدیریت نشریات علمی, 1405; 7(1): 1-19. doi: 10.22098/jfga.2025.17576.1161

Intrinsic Holmes-Thompson volumes and rigidity in Weil bundles

Journal of Finsler Geometry and its Applications
دوره 7، شماره 1، 2026، صفحه 1-19    اصل مقاله (392.42 K)
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.22098/jfga.2025.17576.1161
نویسنده
Tchuiaga Stephane*
Department of Mathematics, University of Buea, South West Region, Cameroon
چکیده
This paper develops a framework for defining intrinsic volumes on manifolds M by leveraging the structure of Weil bundles MA associated with Weil algebras A. We explore constructions for a Finsler-like structure FA primarily on the fibers of MA, 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 FA, an effective Finsler structure FM on the tangent bundle TM is derived. The Busemann-Hausdorff measure dVF associated with FM then provides a volume form on M. We establish foundational results concerning conditions under which a diffeomorphism ø: M → M preserves dVF, linking this to the behavior of its prolongation øA and exploring resulting rigidity phenomena, including a characterization theorem for dVF 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.
کلیدواژه‌ها
Weil Bundles؛ Finsler Geometry؛ Holmes-Thompson Volume؛ Geometric Rigidity؛ Affine Transformations
مراجع
 1. D. Bao, S.S. Chern, and Z. Shen, An introduction to Riemann-Finsler geometry,Springer-Verlag, Berlin, 2000.
2. I. Kol´a˘r, P. W. Michor and J. Slov´ak, Natural Operations in Differential Geometry,Springer, 1993.
3. A. Medvedev, Finsler Structures on Higher-Order Tangent Bundles, Journal of Geometric Analysis, 25(1) (2015), 193-217.
4. D.J. Saunders, The Geometry of Jet Bundles, Cambridge University Press, 1989.
5. S. Tchuiaga, M. Koivogui, and F. Balibuno, Metrizability and dynamics of Weil bundles,Afr. Mat. 36 (95) (2025), https://doi.org/10.1007/s13370-025-01309-6.
6. A. C. Thompson, Minkowski Geometry, Cambridge University Press, 1996. 

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