Geodesic
Newton transformations on null hypersurfaces
Communications in Mathematics, Tome 23 (2015) no. 1, pp. 57-83

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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 in passing, and develop general Minkowski-type formulas for the null hypersurface, supported by some physical models in perfect-fluid space-times.
Classification : 53B30, 53C42, 53Z05
Keywords: Null hypersurfaces; null rigging; Newton transformations; Minkowski integral formulas. 
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Fotsing, Cyriaque Atindogbé and Hans Tetsing. Newton transformations on null hypersurfaces. Communications in Mathematics, Tome 23 (2015) no. 1, pp. 57-83. http://geodesic.mathdoc.fr/item/COMIM_2015__23_1_a4/