Submanifolds and global geometric structures.

Submanifold theory is an important subject in differential geometry. The project aims to study the characterization and construction of certain submanifolds with nice geometric properties, in the sense that they are adapted to a globally defined structure on the ambient space. We plan to consider for example almost complex and Lagrangian submanifolds of nearly Kähler manifolds, Cayley submanifolds of Spin(7)-manifolds and (Hamiltonian) minimal Lagrangian submanifolds of complex projective spaces and of complex hyperquadrics. Although these submanifolds are quite different, there are some (sometimes hidden) relations between them, so it is plausible that they can be studied using similar methods. The main purpose of the project is to put together techniques used by members of the research teams of KU Leuven and Tsinghua University in the past, to see whether they can be applied to study one or several of the above listed families of submanifolds.