In this paper, we study curvature properties of all homogeneous real hypersurfaces in nonflat complex space forms, and determine their minimalities and the signs of their sectional curvatures completely. These properties reflect the sign of the constant holomorphic sectional curvature $c$ of the ambient space. Among others, for the case of $c$ < 0 there exist homogeneous real hypersurfaces with positive sectional curvature and also ones with negative sectional curvature, whereas for the case of $c$ > 0 there do not exist any homogeneous real hypersurfaces with nonpositive sectional curvature.
"Curvature properties of homogeneous real hypersurfaces in nonflat complex space forms." Kodai Math. J. 41 (2) 315 - 331, June 2018. https://doi.org/10.2996/kmj/1530496844