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Stephane, Tchuiaga. (1404). Intrinsic Holmes-Thompson volumes and rigidity in Weil bundles. سامانه مدیریت نشریات علمی, (), 1-19. doi: 10.22098/jfga.2025.17576.1161
Tchuiaga Stephane. "Intrinsic Holmes-Thompson volumes and rigidity in Weil bundles". سامانه مدیریت نشریات علمی, , , 1404, 1-19. doi: 10.22098/jfga.2025.17576.1161
Stephane, Tchuiaga. (1404). 'Intrinsic Holmes-Thompson volumes and rigidity in Weil bundles', سامانه مدیریت نشریات علمی, (), 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, 1404; (): 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
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 28 مهر 1404    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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