Dursun, Uǧur Time-like hypersurfaces of four-dimensional Lorentzian space forms with zero mean curvature. (English) Zbl 1138.53017 Int. Math. Forum 2, No. 53-56, 2687-2699 (2007). Summary: Let \(M\) be a connected space-like surface in a Lorentzian space form \(\widetilde{M}_1^4(c)\). We define a time-like hypersurface \(M^*\) which is the image of a subbundle of the normal bundle of a space-like surface \(M\) spanned by a time-like unit normal vector field \(\xi\) on \(M\) in a four-dimensional Lorentzian space form \(\widetilde{M}_1^4(c)\) under the normal exponential mapping of \(M\) in \(\widetilde{M}_1^4(c)\). We find the equations for a surface \(M\) and a time-like unit normal vector field on \(M\) such that \(M^*\) is a time-like hypersurface in \(\widetilde{M}_1^4(c)\) with zero mean curvature. We also build up some examples. MSC: 53A35 Non-Euclidean differential geometry 53B25 Local submanifolds Keywords:time-like hypersurface; zero mean curvature; Lorentzian space form PDFBibTeX XMLCite \textit{U. Dursun}, Int. Math. Forum 2, No. 53--56, 2687--2699 (2007; Zbl 1138.53017) Full Text: DOI