Four-Dimensional CR Submanifolds of the Homogeneous Nearly Kähler Product Manifold S3×S3

This article presents results on four-dimensional CR submanifolds of the homogeneous nearly Kähler product manifold S3×S3. In the research of CR submanifolds of S3×S3, the most important role in the classification is played by the action of the almost product structure P. Here, the investigation of the action of the almost product structure on the tangent bundle of four-dimensional CR submanifolds of S3×S3 is extended. Classifications are obtained for certain types of submanifolds whose almost complex distribution is almost product invariant, such as the class characterized by a special type of angle functions, as well as those whose tangent bundle is almost product invariant. The previously mentioned classes of four-dimensional CR submanifolds lead to the classification of those submanifolds that are locally usual product manifolds of Lagrangian submanifolds of S3×S3 and curves.