Curvature pinching theorem for minimal surfaces with constant Kaehler angle in complex projective spaces. II (Q685318)

This is a continuation of our paper [ibid. 43, No. 3, 361-374 (1991; Zbl 0725.53063)]. For each integer \(p\) with \(0 \leq p \leq n\), it is known that there exists a full isometric minimal immersion \(\varphi_{n,p}: S^ 2(K_{n,p}) \to P(\mathbb{C})\) of a 2-dimensional sphere of constant Gaussian curvature \(K_{n,p} = 4\rho/(n+2p(n-p))\) into the complex projective \(n\)-space with the Fubini-Study metric of constant holomorphic sectional curvature \(4\rho\). Using \(J\)-invariant first order osculating space, we gave characterization theorems for immersions \(\varphi_{n,p}\) for \(p\leq 3\). The purpose of this paper is to generalize these to the case of \(\varphi_{n,p}\geq 4\). To study the problem, we use \(J\)- invariant higher order osculating spaces to find some scalars defined globally on \(M\), and calculate their Laplacians.