Submanifolds of codimension 3 admitting almost contact metric structure in a complex projective space (Q1841605)

Suppose \(M\) is a codimension three semi-invariant submanifold of \(\mathbb{C} P^{k},\) admitting an almost contact structure. The main result of this paper describes conditions on the third fundamental form under which \(M\) is locally congruent to a homogeneous real hypersurface. A complete and explicit classification of these real hypersurfaces was provided by R. Takagi in earlier work. There are also interesting consequences for the shape tensor, and an example is constructed.