This is a survey article about the recent developments in classifying Randers metrics of scalar flag curvature under an additional condition on the isotropic S-curvature. The authors give an outline of the proof for the classification theorem.

In this paper, we study the curvature features of class homogeneous Randers metrics. For these metrics, first find a reduction criterion to be Berwald metric based on mild restriction their Ricci tensors. Then, prove that every with relatively isotropic (or weak) Landsberg must Riemannian. This provides an extension well-known Deng-Hu theorem proves same result for Berwald-Randers non-zero flag...

Lorentz Invariance violation is a common feature of new physics beyond the standard model. We show that the symmetry of Randers spaces deduces a modified dispersion relation with characteristics of Lorentz Invariance violation. The counterparts of the Lorentz transformation in the Einstein’s Special Relativity are presented explicitly. The coordinate transformations are unitary and form a group...

Eutrophication of estuarine and coastal waters has only been recognised as a potential problem since the early 1980s. This problem is being addressed by the European Union through the implementation of recent water quality legislation, which also calls for an economic analysis relating to its implementation. This paper examines the benefits and costs of reduced eutrophication of the Randers Fjo...

From a rigorous Finsler geometric perspective, we re-examine Holland’s Randers space theory of motion of an electron in flat Minkowski spacetime permeated with an electromagnetic field. Holland’s theory was motivated by analogy with plastic deformation and dislocation in Bravais crystals, through work of D. Bohm on Quantum Mechanics. We develop the anholonomic geometry of a Randers space using ...

In this work we study Randers spacetimes of Berwald type and analyze Pfeifer Wohlfarth's vacuum field equation Finsler gravity for class. We show that in case the is equivalent to vanishing Ricci tensor, analogously Einstein gravity. This implies considered Rutz's coincide scenario. also construct all exact solutions Berwald-Randers gravity, which turn out be composed a CCNV (covariantly consta...

Lorentz Violation is a common feature of Planck-scale phenomenology. We show that the symmetry of Randers spaces deduces a modified dispersion relation, which takes the quantum gravity effects into account. The counterparts of the Lorentz transformation in the Einstein’s Special Relativity are presented explicitly. The coordinate transformations are unitary and form a group. Generators and alge...

We consider a triality between the Zermelo navigation problem, the geodesic flow on a Finslerian geometry of Randers type, and spacetimes in one dimension higher admitting a timelike conformal Killing vector field. From the latter viewpoint, the data of the Zermelo problem are encoded in a (conformally) Painlevé-Gullstrand form of the spacetime metric, whereas the data of the Randers problem ar...

Let $F$ be a left invariant Randers metric on simply connected nilpotent Lie group $N$, induced by Riemannian ${\hat{\textbf{\textit{a}}}}$ and vector field $X$ which is $I_{\hat{\textbf{\textit{a}}}}(M)$-invariant. If the Ricci flow equation has unique solution then, $(N,F)$ soliton if only semialgebraic soliton.