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Full-Text Articles in Physical Sciences and Mathematics
Some Results On Almost Ricci Solitons And Geodesic Vector Fields., Ramesh Sharma
Some Results On Almost Ricci Solitons And Geodesic Vector Fields., Ramesh Sharma
Mathematics Faculty Publications
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.
Almost Ricci Solitons And K-Contact Geometry, Ramesh Sharma
Almost Ricci Solitons And K-Contact Geometry, Ramesh Sharma
Mathematics Faculty Publications
We give a short Lie-derivative theoretic proof of the following recent result of Barros et al. “A compact non-trivial almost Ricci soliton with constant scalar curvature is gradient, and isometric to a Euclidean sphere”. Next, we obtain the result: a complete almost Ricci soliton whose metric g is K-contact and flow vector field X is contact, becomes a Ricci soliton with constant scalar curvature. In particular, for X strict, g becomes compact Sasakian Einstein.