Certain submanifolds of complex space forms

Abstract

After recalling the geometric meaning of the commutativity of the second fundamental tensor of a real hypersurface of a complex space form and its induced almost contact structure, we present some classification theorems for CR submanifolds of maximal CR dimension and submanifolds of real codimension two of complex space forms $${\overline{M}}$$, under the algebraic condition on the second fundamental form of the submanifold and the endomorphism induced from the natural almost complex structure of $${\overline{M}}$$ on the tangent bundle of the submanifold.