A new approach to gradient Ricci solitons and generalizations

摘要: This short note concerns with two inequalities in the geometry of gradient Ricci solitons $(g, f, \lambda )$ on a smooth manifold $M$. These provide some relationships between curvature Riemannian metric $g$ and behavior scalar field $f$ through second order equations satisfied by $\lambda $. We propose several generalizations to setting manifolds endowed linear connections, not necessary type.