geometry of ricci solitons admitting a new geometric vector field

In the present paper, we introduce a new geometric vector field (it will be called semi-killing field) on semi-riemannaian manifolds. a complete classification of semi-killing vector fields on 3-dimensional walker manifolds will be derived. then, we study ricci solitons admitting this new vector field (called semi-killing vector field) as their potential. in riemannain setting, we prove that ricci solitons with semi-killing potential vector field are einstein. our results show that such lorentzian solitons have constant scalar curvature. finally, application of this new structure in theoretical physics has been investigated.