Let $\mathbb{H}P^m$ be the $m$-th quaternionic projective space. What is the smallest integer $N$ such that there exists an embedding
$$
\mathbb{H}P^2\longrightarrow \mathbb{R}^N?
$$
Are there any references?



embedding of quaternionic projective spaces
I. M. James, Lectures on algebraic and differential topology, pp. 134–174, Lecture Notes in Math., Vol. 279, Springer, Berlin, 1972,
Theorems 1.2 and 1.3 show that $$N=13.$$


