Almost Ricci solitons and -contact geometry
R Sharma - Monatshefte für Mathematik, 2014 - Springer
Monatshefte für Mathematik, 2014•Springer
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 gg is K K-contact and flow vector field XX is contact, becomes a Ricci soliton
with constant scalar curvature. In particular, for XX strict, gg becomes compact Sasakian
Einstein.
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 gg is K K-contact and flow vector field XX is contact, becomes a Ricci soliton
with constant scalar curvature. In particular, for XX strict, gg becomes compact Sasakian
Einstein.
Abstract
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 is -contact and flow vector field is contact, becomes a Ricci soliton with constant scalar curvature. In particular, for strict, becomes compact Sasakian Einstein.
Springer
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