×

Time-like hypersurfaces of four-dimensional Lorentzian space forms with zero mean curvature. (English) Zbl 1138.53017

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
PDFBibTeX XMLCite
Full Text: DOI