Real analytic generic mixed type surfaces in Lorentz-Minkowski space admit nontrivial local isometric deformations at lightlike points, and the lightlike normal curvature is extrinsic.
Cartan, Sur la possibilit´ e de plonger un espace riemannien donn´ e d ans un espace eu- clid´ een, Ann
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Isometric deformations of mixed type surfaces in Lorentz-Minkowski space
Real analytic generic mixed type surfaces in Lorentz-Minkowski space admit nontrivial local isometric deformations at lightlike points, and the lightlike normal curvature is extrinsic.