Additive actions on projective hypersurfaces with a finite number of orbits

An induced additive action on a projective variety X ⊆ Pⁿ is a regular action of the group Gₐᵐ on X with an open orbit, which can be extended to a regular action on the ambient projective space Pⁿ. In this work, we classify all projective hypersurfaces admitting an induced additive action with a finite number of orbits.