Bernadett Aradi

University of Debrecen · Department of Geometry, Institute of Mathematics

In this note we generalize a result of J.A. Wolf on Riemannian metrics consistent with absolute parallelisms to the Finslerian case. Along the way we obtain necessary and sufficient conditions for a parallelizable manifold to become a Lie group whose left parallelism is induced by the given one. It also turns out that a Finsler function consistent...

In this paper we study conjugate parallelisms and their conformal changes on Finsler manifolds. We provide sufficient conditions for a Finsler manifold endowed with two conjugate (resp. conformally conjugate) covering parallelisms to become a Berwald (resp. Wagner) manifold. As an application for Lie groups, we give a new proof for a theorem of Lat...

The concept of a parallelism has played a key role in the development of classical geometries and, later, of differential geometry. In a large class of smooth manifolds (including all Lie groups) we have an 'absolute parallelism', which can be described by simple axioms. In Chapter 2 of the Thesis we exhibit a systematic elaboration of the theory o...

In this note we show that a Lie group endowed with a left invariant Finsler function is a generalized Berwald manifold. This observation makes it possible to construct a whole class of generalized Berwald manifolds, thus satisfying a request of Hashiguchi [6]: '.. . find much more interesting examples'. In particular, we show that the Randers Lie g...

This paper considers fundamental issues related to Finslerian isometries, submetries, distance and geodesics. It is shown that at each point of a Finsler manifold there is a distance coordinate system. Using distance coordinates, a simple proof is given for the Finslerian version of the Myers-Steenrod theorem and for the differentiability of Finsle...

We show that the holonomy invariance of a function on the tangent bundle of a manifold, together with very mild regularity conditions on the function, is equivalent to the existence of local parallelisms compatible with the function in a natural way. Thus, in particular, we obtain a characterization of generalized Berwald manifolds. We also constru...