RICCI SOLITONS ON HOPH HYPERSURFACES IN SASAKIAN SPACE FORM

Abstract

We are studying Ricci solitons on Hoph hypersurfaces in Sasakian space formfM2n+1(c). The rst, we prove that Hoph hypersurfaces of a Sasakian space formfM2n+1(c < 1) with two distinct principal curvatures is shrinking and for c 1,Hoph hypersurfaces with two distinct principal curvatures of a Sasakian space formfM2n+1(c) does not admit a Ricci soliton. We show that there is not any Hoph hyper-surfaces with two distinct principal curvatures in a Sasakian space form fM2n+1(c)with a -Ricci soliton (and Ricci soliton) such that potential vector eld is the Reebvector eld.Then we prove that Hoph hypersurfaces in Sasakian space form fM2n+1(c) withc = 1 does not admit a - Ricci soliton with potential vector eld U and we showthat Ricci soliton on Hoph hypersurfaces M in Sasakian space form fM2n+1(c <