Ricci Almost Solitons on Three-Dimensional Quasi-Sasakian Manifolds
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In this paper it is shown that a three-dimensional non-cosymplectic quasi-Sasakian manifold admitting Ricci almost soliton is locally \(\phi \)-symmetric. It is proved that a Ricci almost soliton on a three-dimensional quasi-Sasakian manifold reduces to a Ricci soliton. It is also proved that if a three-dimensional non-cosymplectic quasi-Sasakian manifold admits gradient Ricci soliton, then the potential function is invariant in the orthogonal distribution of the Reeb vector field \(\xi\). We also improve some previous results regarding gradient Ricci soliton on three-dimensional quasi-Sasakian manifolds. An illustrative example is given to support the obtained results.
KeywordsRicci flow Ricci solitons Locally \(\phi \) symmetric Gradient Ricci solitons Quasi-Sasakian manifolds
Mathematics Subject Classification53 C 15 53 D 15
- 15.Hamilton RS (1988) The Ricci flow on surfaces, mathematics and general relativity, vol 71. AMS, ProvidenceGoogle Scholar
- 20.Perelman G (2002) The entropy formula for the Ricci flow and its geometric applications. arxiv:MathDG/0211159 (Preprint)