Some results on almost Ricci solitons and geodesic vector fields
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We show that a compact almost Ricci soliton whose soliton vector field is divergence-free is Einstein and its soliton vector field is Killing. Next we show that an almost Ricci soliton reduces to Ricci soliton if and only if the associated vector field is geodesic. Finally, we prove that a contact metric manifold is K-contact if and only if its Reeb vector field is geodesic.
KeywordsAlmost Ricci soliton Contact metric structure K-contact Einstein Sasakian
Mathematics Subject Classification53C25 53C44 53C21
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