Singularity properties of timelike circular surfaces in Minkowski 3-space

Abstract

The approach of the study is on singularity properties of timelike circular surfaces in Minkowski 3-space. A timelike circular surface is a one-parameter set of Lorentzian circles with stationary radius directing a non-null space curve, which acts as the spine curve, and it has symmetrical properties. In this study, we addressed timelike circular surfaces and gained their geometric and singularity properties such as Gaussian and mean curvatures, comparable with those of ruled surfaces. Consequently, we presented timelike roller coaster surfaces as a special class of timelike circular surfaces. Then, the conditions for timelike roller coaster surfaces to be flat or minimal surfaces are obtained. Meanwhile, we supported the results of the approach with some examples.