Solitons tipo-espaço do fluxo da curvatura média com termo de força em espaços lorentzianos

Abstract

In this work, we study translating solitons with a forcing term immersed in a Lorentzian product space R1 × P n . Under suitable curvature constraints on the curvatures of the Riemannian base P n , we deduce an Omori-Yau maximum principle, and as applications, we get a nonexistence result. Besides, we also prove that any entire spacelike downward-translating graph that never intersects null infinity is mean convex. Furthermore, under suitable assumptions on the base P n , we prove the boundedness of the second fundamental form of such translating solitons. In the last chapter, we classified as translation hypersurfaces those are also translating solitons.