ON SCALAR CURVATURE OF GRADIENTr-ALMOST-NEWTON-EINSTEIN SOLITONS

In this work we establish the concept of r-almost-Newton-Einstein soliton immersed into a Riemannian manifold, which extends in a natural way the notion of Einstein solitons introduced by Catino et al. [8].In this setting, under suitable hypothesis on the potential and soliton functions, we prove nonexistence and characterization results.Also, we proved some triviality results for the compact case and under some conditions we get a constant scalar curvature.