Abstract
In this paper, we focus on a conformally flat Riemannian manifold (Mn,g) of dimension n isometrically immersed into the (n+1)-dimensional light-cone Λn+1 as a hypersurface. We compute the first and the second variational formulas on the volume of such hypersurfaces. Such a hypersurface Mn is not only immersed in Λn+1 but also isometrically realized as a hypersurface of a certain null hypersurface Nn+1 in the Minkowski spacetime, which is different from Λn+1. Moreover, Mn has a volume-maximizing property in Nn+1.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callSimilar Papers
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
