Constant angle surfaces in the Lorentzian warped product manifold $I \times_{f} \mathbb E^2_1$

Authors

UĞUR DURSUN

DOI

10.55730/1300-0098.3326

Abstract

Let $I \times_{f} \mathbb E^2_1$ be a 3-dimensional Lorentzian warped product manifold with the metric $\tilde g = dt^2 + f^2(t) (dx^2 - dy^2)$, where $I$ is an open interval, $f$ is a strictly positive smooth function on $I,$ and $\mathbb E^2_1$ is the Minkowski 2-plane. In this work, we give a classification of all space-like and time-like constant angle surfaces in $I \times_{f} \mathbb E^2_1$ with nonnull principal direction when the surface is time-like. In this classification, we obtain space-like and time-like surfaces with zero mean curvature, rotational surfaces, and surfaces with constant Gaussian curvature. Also, we have some results on constant angle surfaces of the anti-de Sitter space $ \mathbb H^3_1(-1)$.

Keywords

Constant angle surface, warped product, rotational surface, maximal surface, zero mean curvature, Gaussian curvature

First Page

3171

Last Page

3191

Recommended Citation

DURSUN, UĞUR (2022) "Constant angle surfaces in the Lorentzian warped product manifold $I \times_{f} \mathbb E^2_1$," Turkish Journal of Mathematics: Vol. 46: No. 8, Article 8. https://doi.org/10.55730/1300-0098.3326
Available at: https://journals.tubitak.gov.tr/math/vol46/iss8/8