Real hypersurfaces in ℂP2 and ℂH2 with constant scalar curvature

Abstract

Abstract In this paper, Hopf hypersurfaces in a complex projective plane ℂP2(c) or a complex hyperbolic plane ℂH2(c) with constant scalar curvature are classified. For a non-Hopf hypersurface in ℂP2(c) with constant scalar curvature r, it is proved that if the structure vector field is an eigenvector of the Ricci operator, then either r = 7c/2 or r = 3c/2. Moreover, these two cases are determined completely under an additional condition.