Constant Angle Surfaces in the Lorentzian Warped Product Manifold -I×fE2

In this work, we study constant angle space-like and time-like surfaces in the 3-dimensional Lorentzian warped product manifold - I × f E 2 with the metric g ~ = - d t 2 + f 2 ( t ) ( d x 2 + d y 2 ) , where I is an open interval, f is a strictly positive function on I , and E 2 is the Euclidean plane. We obtain a classification of all constant angle space-like and time-like surfaces in - I × f E 2 . In this classification, we determine space-like and time-like surfaces with zero mean curvature, rotational surfaces, and surfaces with constant Gaussian curvature. Also, we obtain some results on constant angle space-like and time-like surfaces of the de Sitter space S 1 3 ( 1 ) .