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Newton transformations on null hypersurfaces. (English) Zbl 1342.53028
Summary: Any rigged null hypersurface is provided with two shape operators: with respect to the rigging and the rigged vector fields respectively. The present paper deals with the Newton transformations built on both of them and establishes related curvature properties. The laters are used to derive necessary and sufficient conditions for higher-order umbilicity and maximality we introduced, and develop general Minkowski-type formulas for the null hypersurface, supported by some physical models in perfect-fluid space-times.

MSC:
53B25 Local submanifolds
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
53B50 Applications of local differential geometry to the sciences
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