- 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
G2 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．