5 papers
On a special class of equidistant sets in the Euclidean space
Ã. Nagy, M. Oláh, M. Stoika +1
An equidistant set in the Euclidean space consists of points having equal distances to both members of a given pair of sets, called focal sets. Since there is no effective formula…
Natural parallel translation and connection associated to navigation data
Asma Mezrag, Zoltan Muzsnay, Csaba Vincze
In this paper, we consider the geometric setting of navigation data and introduce a natural parallel translation using the Riemannian parallelism. The geometry obtained in this way…
An application of Brouwer's fixed-point theorem: continuously differentiable convex functions with gradient of constant norm
Csaba Vincze
As an application of Brouwer's fixed-point theorem we prove that a continuously differentiable convex function with gradient of constant norm is an affine mapping. It is a first-or…
Randers metrics with compatible linear connections: a coordinate-free approach
Márk Oláh, Csaba Vincze
A Randers space is a differentiable manifold equipped with a Randers metric. It is the sum of a Riemannian metric and a one-form on the base manifold. The compatibility of a linear…
On computable classes of equidistant sets: multivariate equidistant functions
Ãbris Nagy, Márk Oláh, Myroslav Stoika +1
An equidistant set in the Euclidean space consists of points having equal distances to both members of a given pair of sets, called focal sets. Having no effective formulas to comp…