LAUSR

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.