مشخصات پژوهش

We are studying Ricci solitons on Hoph hypersurfaces in a Sasakian space form fM2n+1(c). First, we prove that Hoph hypersurfaces of a Sasakian space form fM2n+1(c < 1) with two distinct principal curvatures are shrinking, and for c  1 Hoph hypersurfaces with two distinct principal curvatures of a Sasakian space form fM2n+1(c) do not admit the Ricci soliton. We show that there are no Hoph hypersurfaces with two distinct principal curvatures in a Sasakian space form fM2n+1(c) with an -Ricci soliton (and a Ricci soliton) such that a potential vector field is the Reeb vector field. Then we prove that Hoph hypersurfaces in a Sasakian space form fM2n+1(c) with c = 1 do not admit an - Ricci soliton with a potential vector field U and we show that the Ricci soliton on Hoph hypersurfaces M in a Sasakian space form fM2n+1(c < −3) with a potential vector field U is shrinking the Ricci soliton. Finally, we study the Ricci soliton on locally symmetric hypersurfaces in a Sasakian space form fM2n+1(c) and prove that the Ricci soliton shrins for c < 1. Also, there are no locally symmetric hypersurfaces (M, g) of a Sasakian space form fM2n+1(c  1) with a Ricci soliton.