Positively curved, totally complex submanifolds in the Cayley projective plane
A submanifold of the Cayley projective plane is called totally complex if around each of its points, there exists a local Cayley structure \(\{I_0,\dots{},I_6\}\) such that the tangent space of the submanifold is invariant with respect to \(I_0\) and anti-invariant with respect to \(I_1,\dots{},I_6\). The maximal real dimension of such a submanifold is \(4\). The author proves that a compact totally complex submanifold of maximal dimension in \(CaP^2\) is totally geodesic, hence, by a result of \textit{P. Coulton} and \textit{J. Glazebrook} [Geom. Dedicata 33, 265-272 (1990; Zbl 0698.53036)] it is a \(\mathbb{C} P^2\).
scientific article; zbMATH DE number 1406300