Examples and notes on generalized conics and their applications

Nagy, Ábris and Vincze, Csaba (2010) Examples and notes on generalized conics and their applications. ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS, 26 (2). pp. 359-375. ISSN 0866-0174

Preview

Text amapn26_29.pdf Download (233kB) | Preview

Abstract

Let Γ be a subset of the Euclidean coordinate space. A generalized conic is a set of points with the same average distance from the points γ ∈ Γ. 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 Rn. Such a body induces a Minkowski functional with the elements of G in the linear isometry group. To take the next step consider Rn 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.

Actions (login required)

Edit Item