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

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Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi
Cilt: 18 Sayı: 3
A Note on k-Secant Lines of the Klein Cubic Threefold in PG(4,3)

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

Authors : Ayşe Bayar, Ziya Akça

Pages : 703-712

View : 70 | Download : 129

Publication Date : 2025-12-31

Article Type : Research Paper

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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