Einstein?s metrics and their generalizations have attracted the attention of Mathematicians due to their applications in physics and other natural sciences. The generalization of Einstein metrics is Ricci solitons, ?-Einstein metrics, pseudo-Einstein metrics, and Miao-Tam critical metrics. Given the established non-existence of Einstein real hypersurfaces in a non-flat complex space form ?Mn(c) 2, 13, motivated our investigation into the properties of ?-*Einstein real hypersurface in ?Mn(c). In this paper, we examine the ?-*Einstein Hopf real hypersurface in the complex space form. We prove that there exist ?-*Einstein Hopf real hypersurfaces.
Rani et al. (Wed,) studied this question.
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