Conformal minimal surfaces immersed into \({\mathbb {H}}P^{n}\) (Q1681825)

The paper is devoted to the construction of conformal minimal surfaces and conformal minimal two-spheres in \(\mathbb HP^n\) by the twistor map \(p:\mathbb CP^{2n+1}\to\mathbb HP^n\). The authors are based on \textit{J. Eells} and \textit{J. C. Wood}'s [Adv. Math. 49, 217--263 (1983; Zbl 0528.58007)] conclusion about the composition of a horizontal harmonic map in 1983. First, they characterize horizontal holomorphic surfaces in \(\mathbb CP^5\), then under this characterization, they construct equations of eight families of conformal minimal surfaces in \(\mathbb HP^2\). Then, they study horizontal Veronese sequences in \(\mathbb CP^4\) and \(\mathbb CP^5\), and transform the construction into solving a quadratic equation. Based on this, the authors get some examples of conformal minimal two-spheres in \(\mathbb HP^2\) with constant curvature \(4/5\) and \(4/{13}\).