Journal of the
Korean Mathematical Society JKMS

In this study, we give weighted mean and weighted Gaussian curvatures of two types of timelike general rotational surfaces with non-null plane meridian curves in four-dimensional Minkowski space $\mathbb{E}_{1}^{4}$ with density $e^{\lambda_{1}x^{2}+\lambda_{2}y^{2}+\lambda_{3}z^{2}+\lambda_{4}t^{2}},$ where $\lambda_{i}$ ($i=1,2,3,4$) are not all zero. We give some results about weighted minimal and weighted flat timelike general rotational surfaces in $\mathbb{E}_{1}^{4}$ with density. Also, we construct some examples for these surfaces.

Keywords: Timelike general rotational surface, density, weighted mean curvature, weighted Gaussian curvature

MSC numbers: Primary 53A10, 53A35, 53B30