Rigging Technique for 1−Lightlike Submanifolds
Hans Fotsing Tetsing, African Institute for Mathematical Sciences, Cameroon and Faculty of Sciences, University of Douala, Cameroon
We will discuss riggings on a 1−lightlike submanifold, which have many of the good properties of the Gauss map of non degenerate hypersurfaces. We will also show that for the case of the (n + 2)−dimensional Minskowski space R_1^n+2, the only null Monge hypersurfaces (i.e. graph of a function) x : Σ → R_1^n+2 satisfying the eigenvalue equation ∆x = λx are null hyperplanes. On our way to prove this result, we will show that a smooth function f : R^n+1 ⊃ D → R which is harmonic and whose gradient is of constant norm, is affine.
Anyone can download the two example notebooks
• nbviewer.jupyter.org/github/sagemanifolds/SageManifolds/blob/master/Notebooks/SM degenerate metric.ipynb
• nbviewer.jupyter.org/github/sagemanifolds/SageManifolds/blob/master/Notebooks/SM Schwarzchild horizon degen.ipynb
to see how to use rigging technique in the software SageMath.