A Note on k-Secant Lines of the Klein Cubic Threefold in PG(4,3)

Year 2025, Volume: 18 Issue: 3, 703 - 712

Ayşe Bayar , Ziya Akça

Abstract

In this paper, we developed an algorithm to classify and construct k-secant lines for the Klein cubic threefold F in the projective space PG(4,3). The algorithm identifies secant lines based on their intersections with F, revealing distinct categories of non-secant and k-secant lines. Additionally, we partitioned the point set of F into three subsets, uncovering geometric configurations and forming 5-gons related to perspectively. This analysis offers new insights into the structure of the Klein cubic threefold and its geometric properties.

Keywords

Klein cubic threefold , Projective spaces , Galois field , secant line.

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