Non-existence of conformally flat real hypersurfaces in both the complex quadric and the complex hyperbolic quadric

Abstract In this paper, by applying for a new approach of the so-called Tsinghua principle, we prove the nonexistence of locally conformally flat real hypersurfaces in both the m -dimensional complex quadric $Q^m$ and the complex hyperbolic quadric $Q^{m\ast }$ for $m\ge 3$ .