The feet of orthogonal Buekenhout-Metz unitals
S.G. Barwick, W.-A. Jackson, P. Wild
TL;DR
This paper investigates the geometric properties of the feet of points in orthogonal Buekenhout-Metz unitals within projective planes, revealing their structural types and conditions for forming arcs.
Contribution
It characterizes the set of feet as having types (0,1,2,4) and determines conditions under which these feet form an arc, advancing understanding of unital geometry.
Findings
Feet sets are of types (0,1,2,4)
Conditions for feet to form an arc are established
Analysis of 4-secants in the structure
Abstract
In this article we look at the geometric structure of the feet of an orthogonal Buekenhout-Metz unital U in PG(2,q^2). We show that the feet of each point form a set of type (0,1,2,4). Further, we discuss the structure of any 4-secants, and determine exactly when the feet form an arc.
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Taxonomy
TopicsMathematical functions and polynomials · Mathematical Inequalities and Applications · Mathematics and Applications