Pencils of lines in generalized Laguerre spaces

TL;DR

This paper characterizes subspaces and pencils of lines in generalized Laguerre spaces, exploring their definability and structure within Grassmann spaces, advancing understanding of Laguerre geometry.

Contribution

It introduces new characterizations of subspaces and pencils of lines in multidimensional Laguerre spaces and analyzes their definability within Grassmann structures.

Findings

Subspaces and pencils of lines are characterized in generalized Laguerre spaces.

Definability of conic pencils within Grassmann spaces is established.

Laguerre geometry structures are shown to be definable via pencils of lines.

Abstract

In the paper we characterize subspaces and pencils of lines of generalized (and multidimensional) Laguerre spaces and we consider definability of the structure of "conic" pencils in the Grassmann space of 1-subspaces. We also study definability of the underlying Laguerre geometry in terms of structures of pencils of lines for some, more interesting, systems of pencils.