In this paper we investigate the following question: under what conditions can a second-order homogeneous ordinary differential equation (spray) be the geodesic equation of a Finsler space. We show that the EulerLagrange partial differential system on the energy function can be reduced to a first order system on this same function. In this way we are able to give effective necessary and suffici...

It is still a long-standing open problem in Finsler geometry, there any regular Landsberg metric which not Berwaldian. However, are non-regular metrics The known examples established by G. S. Asanov and Z. Shen. In this paper, we use the Maple program to study some explicit of non-Berwaldian metrics. fact, such kinds very tedious complicated investigate. Nonetheless, packages simplify calculati...

In this paper, we show that the class of R-quadratic Finsler spaces is a proper subset of the class of generalized Douglas-Weyl spaces. Then we prove that all generalized Douglas-Weyl spaces with vanishing Landsberg curvature have vanishing the non-Riemannian quantity H, generalizing result previously only known in the case of R-quadratic metric. Also, this yields an extension of well-known Num...

In this paper we study the geometry of Minkowski plane and obtain some results. We focus on the curve theory in Minkowski plane and prove that the total curvature of any simple closed curve equals to the total Landsberg angle. As the result, the sum of oriented exterior Landsberg angles of any polygon is also equal to the total Landsberg angle, and when the Minkowski plane is reversible, the su...

Abstract For a smooth strongly convex Minkowski norm $F:\mathbb {R}^n \to \mathbb {R}_{\geq 0}$ , we study isometries of the Hessian metric corresponding to function $E=\tfrac 12F^2$ . Under additional assumption that F is invariant with respect standard action $SO(k)\times SO(n-k)$ prove conjecture Laugwitz stated in 1965. Furthermore, describe all between such metrics, and Landsberg Unicorn C...

In this paper, we study the well-known unicorn problem for Finsler metrics. First, prove that every homogeneous Landsberg surface has isotropic flag curvature. Then by using particular form of curvature, a rigidity result on surfaces. Indeed, is Riemannian or locally Minkowskian. Thus, give an affirmative answer to Xu-Deng's conjecture in two-dimensional manifolds.

By unicorns, I am referring to those mythical single-horned horse-like creatures for which there are only rumoured sightings by a privileged few. A similar situation exists in Finsler differential geometry. There, one has the hierarchy Euclidean ⊂ Minkowskian & Riemannian ⊂ Berwald ⊂ Landsberg among five families of metrics, in which the first two inclusions are known to be proper by virtue of ...

Symposium Organizers Rebecca Landsberg & Jim Bonacum (Symposium Co-Chairs) John Martin, Matt Evans, Yash Mhaskar (Moderators) Jo Patterson & Lucia Vazquez (Program & Coordinators) John Martin & Mike Lemke (Abstract Selection) Keenan Dungey (Advertising & Duplication) Jo Patterson & Marc Klingshirn (Announcements & Call for Papers) Harshavarden Bapat & Wayne Gade (Budget & Expenses) Harshavarden...