Real Hypersurfaces in Complex Grassmannians of Rank Two

Abstract

It is known that there does not exist any Hopf hypersurface in complex Grassmannians of rank two of complex dimension 2m with constant sectional curvature for m≥3. The purpose of this article is to extend the above result, and without the Hopf condition, we prove that there does not exist any locally conformally flat real hypersurface for m≥3.

Keywords

• complex Grassmannians of rank two
• real hypersurface
• locally conformally flat
• constant sectional curvature