Certain submanifolds of real codimension two of a complex projective space

Abstract

We prove a classification theorem for a submanifold of real codimension two of a complex projective space, which is not its totally geodesic complex hypersurface, under the condition h(FX, Y)+h(X, FY) = 0, where h is the second fundamental form of the submanifold and F is the endomorphism induced from the almost complex structure J on the tangent bundle of the submanifold.