Examples and notes on generalized conics and their applications

Acta Mathematica Academiae Paedagogicae Nyíregyháziensis

Á. Nagy¹  Cs. Vincze¹ 

[1] University of Debrecen

关键词: Berwald manifolds;   

DOI  :  

学科分类：数学（综合）

来源: Academia Paedagogica Nyiregyhaziensis. Acta Mathematica

【 摘 要 】

Let $Gamma$ be a subset of the Euclidean coordinate space. A generalized conic is a set of points with the same average distance from the points $gamma in Gamma$. First of all we consider some realizations of this concept. Basic properties will be given together with an application. It is a general process to construct convex bodies which are invariant under a fixed subgroup $G$ of the orthogonal group in $mathbb{R}^n$. Such a body induces a Minkowski functional with the elements of $G$ in the linear isometry group. To take the next step consider $mathbb{R}^n$ as the tangent space at a point of a connected Riemannian manifold $M$ and $G$ as the holonomy group. By the help of the method presented here $M$ can be changed into a non-Riemannian Berwald manifold with the same canonical linear connection as that of $M$ as a Riemannian manifold. Indicatrices with respect to the Finslerian fundamental function are generalized conics with respect to the Euclidean norm induced by the Riemannian metric.

【 授权许可】

Unknown