$HS_{r}$-valued Gauss maps and umbilic spacelike surfaces of codimension two

Details $HS_{r}$-valued Gauss maps and umbilic spacelike surfaces of codimension two $HS_{r}$-valued Gauss maps and umbilic spacelike surfaces of codimension two

2011-02-12

arxiv.org/abs/1102.2527v2

Mathematics

Differential Geometry

15 pages

Scientific paper

To study spacelike surfaces of codimension two in the Lorentz-Minkowski space $\Bbb R^{n+1}_1,$ we construct a pair of maps whose values are in $HS_r:=H_+^n(\textbf v,1)\cap \{x_{n+1}=r\},$ called $\textbf n_r^{\pm}$-Gauss maps. It is showed that they are well-defined and useful to study practically flat as well as umbilic spacelike surfaces of codimension two in $\Bbb R^{n+1}_1.$

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