Curvature pinching for totally real submanifolds of a complex projective space (Q1975890)

The main result in this paper gives a classification of \(n\)-dimensional compact totally real minimal submanifolds isometrically immersed in complex projective space \(\mathbb{C} P^n(c)\) such that the scalar curvature \(\tau\) is constant and \(16\tau\geq 2n(n-2)c\). This result answers in a positive way a conjecture stated by K. Ogiue. The classification coincides with the one obtained by \textit{S. Montiel}, \textit{A. Ros} and \textit{F. Urbano} [Math. Z. 191, 537-548 (1986; Zbl 0563.53046)] when the above curvature conditions are replaced by \(16S\geq 3(n-2)c\), \(S\) being the Ricci curvature.