A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
We study the behavior of geodesics on a Randers surface of revolution. The main tool is the extension of Clairaut relation from Riemannian case to the Randers case. Moreover, we show that our Randers surface of revolution can be embedded in a Minkowski space as hypersurface.
By a Randers' structure on a manifold M we mean a Finsler structure L∗=L+α, where L is a Riemannian structure and α is a 1-form on M. This structure was first introduced by Randers ~\cite{[8]} from the standpoint of general relativity. In this paper, we replace L by a Finsler structure, calling the resulti…
Study classifies holonomy groups of projectively flat Randers surfaces.
problem Classifying holonomy groups of Randers surfaces.
method Investigation of holonomy structure of Randers surfaces, classification of holonomy groups.
result Holonomy group of simply connected non-Riemannian projectively flat Finsler two-manifolds is maximal and isomorphic to the circle diffeomorphism group.
In this paper, we study Randers metrics and find a condition on Ricci tensor of these metrics to be Berwaldian. This generalize Shen's Theorem which says: every R-°at complete Randers metric is locally Minkowskian. Then we find a necessary and sufficient condition on Ricci tensor under which a Randers metric of scalar …
A left invariant Z-Randers metric on the five-dimensional Heisenberg group is a left invariant Randers metric with deformation vector from the center of the Heisenberg algebra. In this note we prove that for every left invariant Z-Randers metric on the five-dimensional Heisenberg group there exist flags of strictly neg…
In the present paper, the flag curvature of invariant Randers metrics on homogeneous spaces and Lie groups is studied. We first give an explicit formula for the flag curvature of invariant Randers metrics arising from invariant Riemannian metrics on homogeneous spaces and, in special case, Lie groups. We then study Ran…
Characterizes C-projective vector fields on Randers spaces.
problem Characterizing C-projective vector fields on Randers spaces.
method Using a non-Riemannian quantity ${fΞ}$, it is shown that ${fΞ}$ is invariant for C-projective vector fields and the dimension of the algebra of C-projective vector fields is at most n(n+2).
result An n-dimensional Randers space has a C-projective algebra of maximum dimension n(n+2) if and only if it is locally Minkowskian or (up to re-scaling) locally isometric to the generalized Funk metric.
We correct a mistake in Shen Yibing, Yu Yaoyong, On Projectively Related Randers Metrics, International Journal of Mathematics 19}(2008), no. 5, 503--520, and prove the natural generalization of the projective Lichnerowicz-Obata conjecture for Randers metrics.
Let G be a Lie group equipped with a left invariant Randers metric of Berward type F, with underlying left invariant Riemannian metric g. Suppose that F and g are lifted Randers and Riemannian metrics arising from F and g on the tangent Lie group TG by vertical and complete lifts…
In this paper, we study Clifford-Wolf translations of homogeneous Randers metrics on spheres. It turns out that we can present a complete description of all the Clifford-Wolf translations of all the homogeneous Randers metrics on spheres. The most important point of this paper is that a new phenomena surfaces. Namely, …
In this paper we argue that when gauge invariance is taken into consideration, there is no consistent geometric framework of Finsler class that can accommodate Randers type spaces. In this context, an alternative non-Finslerian framework for Randers spacetimes compatible with gauge invariance is introduced.
The contribution of this paper is two-fold. The first one is to derive a simple formula of the mean curvature form for a hypersurface in the Randers space with a Killing field, by considering the Busemann-Hausdorff measure and Holmes-Thompson measure simultaneously. The second one is to obtain the explicit local expres…
In this article we review the recent results about the flag curvature of invariant Randers metrics on homogeneous manifolds and by using a counter example we show that the formula which obtained for the flag curvature of these metrics is incorrect. Then we give an explicit formula for the flag curvature of invariant Ra…
We obtain some results in both Lorentz and Finsler geometries, by using a correspondence between the conformal structure (Causality) of standard stationary spacetimes on M=R×S and Randers metrics on S. In particular, for stationary spacetimes, we give a simple characterization of when they are causally conti…
In the year 1984 Shibata investigated the theory of a change which is called a β-change of a Finsler metric. On the other hand in 1985 a systematic study of geometry of hypersurfaces in Finsler spaces was given by Matsumoto. In the present paper is to devoted to the study of a condition for a Randers conformal chang…
In 2D, Finsler metrics are Douglas and generalized Berwald if they are Berwald or Randers.
problem Characterizing Finsler metrics in 2D that are both Douglas and generalized Berwald.
method Proof that in dimension two, a Finsler metric is both Douglas and generalized Berwald if and only if it is Berwald or a Randers metric α+β with specific properties.
result Finsler metrics in 2D are Douglas and generalized Berwald if they are Berwald or Randers metrics with specific properties.
In the present paper we study Randers metics of Berwald type on simply connected 4-dimensional real Lie groups admitting invariant hypercomplex structure. On these spaces, the Randers metrics arising from invariant hyper-Hermitian metrics are considered. Then we give explicit formulas for computing flag curvature of th…