Gauss map singularities of inversion hypersurface in R^{n+1}

This paper mainly studies the singularities of Gauss map of inversion hypersurface in $R^{n+1}$. The geometry of inversion hypersurface in $R^{n+1}$ and its Gauss map are given. Using the lagrangian and Legendrian singularity theory, the singularities of Gauss map of inversion hypersurface are classified and plotted.