- Surface theory：minimal surfaces, CMC surfaces, stability, deformations
holomorphic curves, harmonic maps

- Hypersurface theory：Dupin hypersurfaces，isoparametric hypersurfaces
classification, orbit geometry, Lie contact geometry

- Special geometry: holonomy groups, special Lagrangian submanifolds
G

_{2}metrics, Ricci flat metrics, calibrations - Theory of integrable systems related with surface theory and hypersurface theory．
Periodic Toda equations, the wave equations

- G-structures：Lie contact structure，Cartan-Tanaka theory
Cartan-Tanaka connection, curvature, graded Lie algebras of the 2nd kind．