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Abstract
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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.
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