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.

中文翻译：

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D-同位变形 K-接触 Ricci 几乎孤子

如果 K 接触流形 (M, g) 和 D 同位变形 K 接触流形 $$(M,{\bar{g}})$$ 都是具有相同关联矢量场 V 的 Ricci 几乎孤子，那么我们证明 (i) (M, g) 和 ( $$M, {\bar{g}}$$ ) 都是 D-homothetically 固定 $$\eta $$ -Einstein Ricci 孤子，并且 (ii) V 保留$$\phi $$ 。我们还表明，如果一个完整的 K 接触 Ricci 几乎孤子 (M, g, V) 的相关矢量场 V 是一个射影矢量场，那么 V 是 Killing 并且 (M, g) 是紧 Sasakian 和收缩。最后，我们表明任何向量场的散度在 D 同位变形下都是不变的。