Totally Umbilical Hypersurfaces of Lorentzian Reducible Spaces

Abstract We investigate totally umbilical hypersurfaces in Lorentzian reducible spaces, focusing on their classification and geometric properties. We explore conditions for the existence of proper totally umbilical hypersurfaces in a $$(n+1)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> -dimensional Lorentzian reducible manifold and provide explicit examples, especially in the three-dimensional case. Moreover, in this special case, we determine a general condition characterizing minimal and CMC surfaces and describe some examples.