The Cayley projective plane can be realized as the homogeneous space $F_4/Spin(9)$. In this way one can compute the curvature of this symmetric space in terms of a suitable orthonormal basis and the Lie brackets of the basic vectors. But is there any elegant expression for the curvature of $\mathbb{OP}^2$ which is independent of this homogeneous description due to the fact that $\mathbb{OP}^2$ is a rank one symmetric space?

The Cayley projective plane can be realized as the compact homogeneous space $F_4/\mathrm{Spin}(9)$. In this way one can compute the curvature of this symmetric space in terms of a suitable orthonormal basis and the Lie brackets of the basic vectors. But is there any elegant expression for the curvature of $\mathbb{OP}^2$ which is independent of this homogeneous description due to the fact that $\mathbb{OP}^2$ is a rank one symmetric space?

The Cayley projective plane can be realized as the homogeneous space $F_4/Spin(9)$. In this way one can compute the curvature of this symmetric space in terms of a suitable orthonormal basis and the Lie brackets of the basic vectors. But is there any elegant expression for the curvature of $CaP^2$ which is independent of this homogeneous description due to the fact that $CaP^2$ is a rank one symmetric space?

The Cayley projective plane can be realized as the homogeneous space $F_4/Spin(9)$. In this way one can compute the curvature of this symmetric space in terms of a suitable orthonormal basis and the Lie brackets of the basic vectors. But is there any elegant expression for the curvature of $\mathbb{OP}^2$ which is independent of this homogeneous description due to the fact that $\mathbb{OP}^2$ is a rank one symmetric space?