Rigidity and Classification of Ricci Solitons on Lorentzian Hypersurfaces with Concircular Vector Fields on Minkowski Space

This paper examines the classification of Lorentzian hypersurfaces in Minkowski space, specifically focusing on those that are characterized as good or bad and that admit Ricci solitons with a concircular vector field. First, we demonstrate that Ricci solitons of this nature do not exist in Lorentzian spaces that have non-zero sectional curvature. Additionally, we show that the shape operator can be expressed in specific canonical forms.