Dimensional dual hyperovals in classical polar spaces

TL;DR

This paper proves that n-dimensional dual hyperovals can only exist in one specific classical polar space of rank n when n is even, resolving a previously open question.

Contribution

It establishes a non-existence result for dual hyperovals in most classical polar spaces of even rank, answering a question by Yoshiara.

Findings

Dual hyperovals do not exist in most classical polar spaces of even rank

Existence is limited to a unique classical polar space for even n

The result clarifies the structure of dual hyperovals in polar spaces

Abstract

In this paper we show that n-dimensional dual hyperovals cannot exist in all but one classical polar space of rank n if n is even. This resolves a question posed by Yoshiara.