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

Abstract

In this work, we study constant angle space-like and time-like surfaces in the 3-dimensional Lorentzian warped product manifold - I× fE2 with the metric g~ = - d t2+ f2(t) (d x2+ d y2) , where I is an open interval, f is a strictly positive function on I, and E2 is the Euclidean plane. We obtain a classification of all constant angle space-like and time-like surfaces in - I× fE2. 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 S13(1).