arXiv research

In 2D, Finsler metrics are Douglas and generalized Berwald if they are Berwald or Randers.

PhD dissertation on Finsler geometry and gravity, focusing on Berwald spaces and exact solutions.

Establishes conditions for Berwald Finsler geometries.

Paper studies curvature in Finsler geometry, proving curvature constancy under isotropy.

Locally classifies 4D spherical symmetric Finsler spaces.

The paper studies Berwald scalar curvature properties in Finsler geometry.

Based on a self-contained, coordinate-free exposition of the necessary concepts and tools of spray and Finsler geometry (with detailed proofs), we derive new results among others on the consequences of the direction-independence of the Landsberg tensor and the stretch tensor of a Finsler manifold. We show that an at le…

Jebsen-Birkhoff theorem extended to Berwald spacetimes.

Study Finsler metrics with vanishing Landsberg curvature.

Study on Berwald-Weyl curvature with projective invariance and vanishing results.

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 equivalent to the Berwald metric leaves invariant the indicatrix of th Finsler metr…

For a $2$-dimensional non-flat spray we associate a Berwald frame and a $3$-dimensional distribution that we call the Berwald distribution. The Frobenius integrability of the Berwald distribution characterises the Finsler metrizability of the given spray. In the integrable case, the sought after Finsler function is pro…

Paper studies Minkowskian product of Finsler manifolds and their connections.

Paper establishes a relation between Berwald scalar curvature and S-curvature.

Recently the present authors introduced a general class of Finsler connections which leads to a smart representation of connection theory in Finsler geometry and yields to a classification of Finsler connections into the three classes. Here the properties of one of these classes namely the Berwald-type connections whic…

New findings show Berwald Finsler spacetimes cannot be metrized.

In this paper, we characterize locally dually flat and Antonelli $m$-th root Finsler metrics. Then, we show that every $m$-th root Finsler metric of isotropic mean Berwald curvature reduces to a weakly Berwald metric.

Characterizes Kähler-Berwald metrics on complex manifolds.

New splitting theorem for weighted Finsler spacetimes without Berwald condition.

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 preserves the Finsler function

Researchers generalize cosmological models using Finsler geometry.

New exact spherically symmetric vacuum solutions found in Finsler gravity.

In this paper, we construct a new class of Finsler manifolds called generalized isotropic Berwald manifolds which is an extension of the class of isotropic Berwald manifolds. We prove that every generalized isotropic Berwald manifold is a generalized Douglas-Weyl manifold. On a compact generalized isotropic Berwald man…

In this paper we introduce a natural definition for the affine maps between two Finsler manifolds $(M, F)$ and $(N,\tilde F)$ and we give some geometrical properties of these affine maps. Starting from the equations of the affine maps, we construct a natural Berwald-Riemann-Lagrange geometry on the 1-jet space $J^1(TM;…

The paper proves rigidity results for non-positively curved homogeneous Finsler metrics.

After summarizing some necessary preliminaries and tools, including Berwald derivative and Lie derivative in pull-back formalism, we present ten equivalent conditions, each of which characterizes Berwald manifolds among Finsler manifolds. These range from Berwald's classical definition to the existence of a torsion-fre…

Analyzing static solutions in Finsler gravity, extending known results.

Calculates S-curvature and mean Berwald curvature in homogeneous Finsler spaces.

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 Finsler metrics in this class. Finally we show that on this class of Finsler met…

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 suitable for studying optimal regularity of the fundamental tensor, nevertheless, we …

The paper classifies Landsberg spherically symmetric Finsler metrics in various dimensions.

Study curvature of complex Finsler metrics on Lie groups.

The paper classifies Landsberg metrics on a 2D Lie group and proves a conjecture.

Finsleroid-Finsler metrics form an important class of singular (y-local) Finslerian metrics. They were introduced by G. S. Asanov in 2006. As a special case Asanov produced examples of Landsberg spaces of dimension at least three that are not of Berwald type. These are called Unicorns [5]. The existence of regular (y -…

Berwald metrics are particular Finsler metrics which still have linear Berwald connections. Their complete classification is established in an earlier work, [Sz1], of this author. The main tools in these classification are the Simons-Berger holonomy theorem and the Weyl-group theory. It turnes out that any Berwald metr…

New insights into metrizability of SO(3)-invariant connections, linking Riemann and Finsler structures.

In this paper, we mainly establish a Cheeger type finiteness theorem for Berwald manifolds. In order to do this, we study the injectivity radius and the convex radius of a Finsler manifold. A Cheeger type estimate on injectivity radii for Finsler manifolds is given and the existence of the center of mass of a Berwald m…

In this paper, we study a class of Finsler metrics called general $(α,β)$-metrics, which are defined by a Riemannian metric $α$ and a $1$-form $β$. We classify this class of Finsler metrics with isotropic Berwald curvature under certain condition.

Study of Randers spacetimes and their Finsler gravity solutions.

On the product of two Finsler manifolds M1 M2, we consider the twisted metric F which is construct by using Finsler metrics F1 and F2 on the manifolds M1 and M2, respectively. We introduce horizontal and vertical distributions on twisted product Finsler manifold and study Creducible and semi-C-reducible properties of t…

By performing required evaluations, we show that in the Finsleroid-regular space the Landsberg-space condition just degenerates to the Berwald-space condition (at any dimension number $N\ge2$). Simple and clear expository representations are obtained. Due comparisons with the Finsleroid-Finsler space are indicated. Key…

Finsleroid-Finsler metrics form an important class of singular (y-local) Finsler metrics. They were introduced by G. S. Asanov [2] in 2006. As the special case of the general construction Asanov produced singular (y - local) examples of Landsberg spaces of dimension at least three that are not of Berwald type. The exis…

The paper characterizes complex Finsler metrics invariant under U(n) and their properties.

The problem of conformal transformation and conformal flatness of Finsler spaces has been studied by so many researchers $\left[ 6,16,17,20,21\right] .$ Recently, Prasad et. al $\left[ 19\right]$ have studied three dimensional conformally flat Landsberg and Berwald spaces and have given some important results. The pur…

In this paper, we consider doubly warped product (DWP) Finsler manifolds with some non-Riemannian curvature properties. First, we study Berwald and isotropic mean Berwald DWP-Finsler manifolds. Then we prove that every proper Douglas DWP-Finsler manifold is Riemannian. We show that a proper DWP-manifold is Landsbergian…

Study finds first integrals in Finsler metrics with vanishing χ-curvature.

Characterizes two-dimensional generalized Berwald metrics with vanishing S-curvature.

In this paper, we investigate the two-dimensional complex Finsler manifolds. The tools of this study are the complex Berwald frames and the Chern-Finsler connection with respect to these frames.