The nullity of compact minimal real hypersurfaces in a complex projective space (Q1335287)

Let \(\mathbb{C} P^ n\) be the \(n\)-dimensional complex projective space with the Fubini-Study metric of constant holomorphic sectional curvature 4, and \(M\) be a compact oriented minimal real hypersurface in \(\mathbb{C} P^ n\). In this paper, the author proves the following theorem: The nullity \(\text{nul}(M)\) of \(M\) in \(\mathbb{C} P^ n\) satisfies an inequality \(\text{nul}(M) \geq 2n\), where the equality holds if and only if \(M\) is the geodesic hypersphere \(M^ C_{0,n-1}\).