We establish the concept of $r$-almost Newton-Ricci soliton immersed into a Lorentzian manifold, which extends in a natural way the almost Ricci solitons introduced by Pigola, Rigoli, Rimoldi and Setti in . In this setting, under suitable hypothesis on the potential and soliton functions, we obtain nonexistence and rigidity results. Some interesting examples of these new geometric objects are also given.
"$r$-Almost Newton-Ricci solitons immersed in a Lorentzian manifold: examples, nonexistence and rigidity." Kodai Math. J. 43 (1) 42 - 56, March 2020. https://doi.org/10.2996/kmj/1584345687