Related papers: Finsleroid-regular space. Landsberg-to-Berwald imp…
This thesis contains an introduction to the method of average in Finsler geometry. The method is applied to Berwald spaces, obtaining geodesic rigidity conditions. We prove that the Levi-Civita connection of any Riemannian metric affine…
Every Finsler metric naturally induces a spray but not so for the converse. The notion for sprays of scalar (resp. isotropic) curvature has been known as a generalization for Finsler metrics of scalar (resp. isotropic) flag curvature. In…
We prove that the Ricci scalar curvature and the Berwald scalar curvature of a two-dimensional Finsler space, considered over a vector field on the 3-dimensional flat space, are naturally related to 2-dimensional electro-capillary phenomena…
We prove existence of harmonic coordinates for the nonlinear Laplacian of a Finsler manifold and apply them in a proof of the Myers--Steenrod theorem for Finsler manifolds. Different from the Riemannian case, these coordinates are not…
We show that monochromatic Finsler metrics, i.e., Finsler metrics such that each two tangent spaces are isomorphic as normed spaces, are generalized Berwald metrics, i.e., there exists an affine connection, possibly with torsion, that…
In this paper, studying the inverse problem, we establish a curvature compatibility condition on a spherically symmetric Finsler metric. As an application, we characterize the spherically symmetric metrics of scalar curvature. We construct…
For a Finsler metric $F$, we introduce the notion of $F$-covariant coefficients $H_i$ of the geodesic spray of $F$ (Def. 3.1). We study some geometric consequences concerning the objects $H_i$. If the $F$-covariant coefficients $H_i$ are…
A systematic approach has been developed to encompass the Minkowski-type extension of Euclidean geometry such that a one-vector anisotropy is permitted, retaining simultaneously the concept of angle. For the respective geometry, the…
The study of curvature properties of homogeneous Finsler spaces with $(\alpha, \beta)$-metrics is one of the central problems in Riemann-Finsler geometry. In the present paper, the existence of invariant vector fields on homogeneous Finsler…
In this paper, we study a class of Finsler metrics which contains the class of Berwald metrics as a special case. We prove that every Finsler metric in this class is a generalized Douglas-Weyl metric. Then we study isotropic flag curvature…
In this short paper, we study a symmetric covariant tensor in Finsler geometry, which is called the mean Berwald curvature. We first investigate the geometry of the fibres as the submanifolds of the tangent sphere bundle on a Finsler…
It is still a long-standing open problem in Finsler geometry, is there any regular Landsberg metric which is not Berwaldian. However, there are non-regular Landsberg metrics which are not Berwladian. The known examples are established by G.…
We prove generalized lower Ricci curvature bounds for warped products over complete Finsler manifolds. On the one hand our result covers a theorem of Bacher and Sturm concerning euclidean and spherical cones. On the other hand it can be…
In this short paper, we prove that a Finsler manifold with vanishing Berwald scalar curvature has zero $\mathbf{E}$-curvature. As a consequence, Landsberg manifolds with vanishing Berwald scalar curvature are Berwald manifolds. This…
In this paper, we investigate the existence of parallel 1-forms on specific Finsler manifolds. We demonstrate that Landsberg manifolds admitting a parallel 1-form have a mean Berwald curvature of rank at most $n-2$. As a result, Landsberg…
Given a Finsler space, we introduce a system of partial differential equations, called the Landsberg equation. Based on a careful analysis of the Landsberg equation and the observation that the solution space is invariant under the linear…
In this paper, the Cartan tensors of the $(\alpha,\beta)$-norms are investigated in details. Then an equivalence theorem of $(\alpha,\beta)$-norms is proved. As a consequence in Finsler geometry, general $(\alpha,\beta)$-metrics on smooth…
In this paper, first we prove the existence of invariant vector field on a homogeneous Finsler space with infinite series $(\alpha, \beta)$-metric and exponential metric. Next, we deduce an explicit formula for the the $S$-curvature of…
We show that which that for a Berwald structure, any Riemannian structure that is preserved by the Berwald connection leaves the indicatrix invariant under horizontal parallel transport. We also obtain the converse result: if $({\bf M},F)$…
We study a special class of Finsler metrics which we refer to as Almost Rational Finsler metrics (shortly, AR-Finsler metrics). We give necessary and sufficient conditions for an AR-Finsler manifold $(M,F)$ to be Riemannian. The rationality…