In contrast to the Gauss equation which when expressed in the components of the second fundamental form gives quadratic equations, the Tsinghua principal gives linear equations for the components of the second fundamental form. Recent applications of this principal lead to classification (or at least allow significant progress) in the study of:

-the classification of constant curvature immersions in the nearly kaehler $S^3 \times S^3$

-the classification of constant curvature immersions in the complex quadric $Q^n$

-the classification of constant curvature immersions in the complex hyperbolic quadric $Q^n$

-the classification of affine hyperspheres $M=M_1(c_1) \times M_2(c_2)$

-the classification of minimal lagrangian immersions $M=M_1(c_1) \times M_2(c_2)$ in complex space forms

-the classification of lagrangian immersions in the nearly Kaehler $S^6$ which are a warped product with 1 dimensional base

-the classification of hypersurfaces in $\mathbb R^{n+1}$ which are a warped product of  1 dimensional base with an (n-1) manifold with constant sectional curvature

-the study affine hypersurfaces with constant sectional curvature

-the study of conformally flat affine hyperspheres