## Tohoku Mathematical Journal 2009 June SECOND SERIES VOL. 61, NO. 2

 Tohoku Math. J. 61 (2009), 205-212

Title RICCI SOLITONS AND REAL HYPERSURFACES IN A COMPLEX SPACE FORM

Author Jong Taek Cho and Makoto Kimura

(Received June 19, 2008, revised August 26, 2008)
Abstract. We prove that a real hypersurface in a non-flat complex space form does not admit a Ricci soliton whose potential vector field is the Reeb vector field. Moreover, we classify a real hypersurface admitting so-called “$\eta$-Ricci soliton” in a non-flat complex space form.

2000 Mathematics Subject Classification. Primary 53C20; Secondary 53C15, 53C25.