Proof of Laugwitz Conjecture and Landsberg Unicorn Conjecture for Minkowski norms with -symmetry

DOI10.4153/S0008414X21000304zbMath1505.53055arXiv2007.15888WikidataQ113692061 ScholiaQ113692061MaRDI QIDQ5046567

Ming Xu, Vladimir S. Matveev

Publication date: 8 November 2022

Published in: Canadian Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.15888

zbMATH Keywords

Legendre transformationMinkowski normHessian isometryLaugwitz conjectureLandsberg unicorn conjecture

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Local differential geometry of Finsler spaces and generalizations (areal metrics) (53B40) Minkowski geometries in nonlinear incidence geometry (51B20)

Related Items (2)

Naturally reductive \((\alpha_1, \alpha_2)\) metrics ⋮ Parallel translations for a left invariant spray

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Binet-Legendre metric in Finsler geometry
• On semi-C-reducibility, T-tensor=0 and S4-likeness of Finsler spaces
• Homogeneous Riemannian spaces of four dimensions
• On \(n\)-dimensional homogeneous spaces of Lie groups of dimension greater than \({1\over 2}n(n-1)\)
• On Finsler spaces with Randers' metric and special forms of important tensors
• Finslerian metric functions over the product \(\mathbb{R}\times M\) and their potential applications
• Finsler cases of GF-space
• An equivalence theorem of a class of Minkowski norms and its applications
• Left invariant Clifford-Wolf homogeneous \(\alpha, \beta)\)-metrics on compact semisimple Lie groups
• On a class of almost regular Landsberg metrics
• Finsleroid-Finsler spaces of positive-definite and relativistic types
• Über die Finslerräume mit \(S_{ijkl} = O\)
• \((\alpha_1,\alpha_2)\)-metrics and Clifford-Wolf homogeneity
• Über Finslersche und Cartansche Geometrie. IV. Projektivkrümmung allgemeiner affiner Räume und Finslerscher Räume skalarer Krümmung
• On Strongly Convex Indicatrices in Minkowski Geometry
• Finsler spaces of $(\alpha,\beta)$ type and semi-C-reducibility
• On a Class of Landsberg Metrics in Finsler Geometry
• On "Regular Landsberg metrics are always Berwald" by Z. I. Szabo
• Unique decomposition of Riemannian manifolds
• Applications of Nijenhuis geometry II: maximal pencils of multi-Hamiltonian structures of hydrodynamic type
• The Landsberg equation of a Finsler space
• Geometry of Hessian Structures
• A Theorem on Homogeneous Functions
• On n-Dimensional Riemannian Spaces Admitting a Group of Motions of Order n(n-1)/2 + 1
• Global affine differential geometry of hypersurfaces

This page was built for publication: Proof of Laugwitz Conjecture and Landsberg Unicorn Conjecture for Minkowski norms with -symmetry