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- Title
RICCI SOLITONS ON HOPH HYPERSURFACES IN A SASAKIAN SPACE FORM.
- Authors
Nazari, Zahra; Abedi, Esmail
- Abstract
We are studying Ricci solitons on Hoph hypersurfaces in a Sasakian space form M2n+1(c). First, we prove that Hoph hypersurfaces of a Sasakian space form M2n+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 M2n+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 M2n+1(c) with an η-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 M2n+1(c) with c = 1 do not admit an η- Ricci soliton with a potential vector field U and we show that the Ricci soliton on Hoph hypersurfaces M in a Sasakian space form M2n+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 M2n+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 M2n+1(c ≥ 1) with a Ricci soliton.
- Subjects
RICCI flow; HYPERSURFACES; TOPOLOGICAL spaces
- Publication
Facta Universitatis, Series: Mathematics & Informatics, 2017, Vol 32, Issue 3, p387
- ISSN
0352-9665
- Publication type
Article
- DOI
10.22190/FUMI1703387N