Abstract
If a K-contact manifold (M, g) and a D-homothetically deformed K-contact manifold \((M,{\bar{g}})\) are both Ricci almost solitons with the same associated vector field V, then we show (i) that (M, g) and (\(M, {\bar{g}}\)) are both D-homothetically fixed \(\eta \)-Einstein Ricci solitons, and (ii) V preserves \(\phi \). We also show that, if the associated vector field V of a complete K-contact Ricci almost soliton (M, g, V) is a projective vector field, then V is Killing and (M, g) is compact Sasakian and shrinking. Finally, we show that the divergence of any vector field is invariant under a D-homothetic deformation.
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The authors are grateful to the referee for a couple of valuable suggestions.
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Gangadharappa, N.H., Sharma, R. D-homothetically Deformed K-contact Ricci Almost Solitons. Results Math 75, 124 (2020). https://doi.org/10.1007/s00025-020-01250-z
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DOI: https://doi.org/10.1007/s00025-020-01250-z