On solitons in statistical geometry

摘要

We introduce the notion of Killing soliton and study its properties. For the particular cases when the g-dual vector field of η is of Jacobi-type, torse-forming, conformal Killing and 2-Killing respectively, we obtain conditions that must be satisfied by the two functions that define the soliton. Moreover, we provide necessary and sufficient conditions for an almost η-Ricci and almost η-Einstein soliton to give rise to a statistical structure.