Geometry of isoparametric null hypersurfaces of Lorentzian manifolds
J. Korean Math. Soc. 2020 Vol. 57, No. 1, 195-213
https://doi.org/10.4134/JKMS.j190001
Published online January 1, 2020
Samuel Ssekajja
University of Witwatersrand
Abstract : We define two types of null hypersurfaces as; {\it isoparametric} and {\it quasi isoparametric} null hypersurfaces of Lorentzian space forms, based on the two shape operators associated with a null hypersurface. We prove that; on any screen conformal isoparametric null hypersurface, the screen geodesics lie on circles in the ambient space. Furthermore, we prove that the screen distributions of isoparametric (or quasi isoparametric) null hypersurfaces with at most two principal curvatures are generally Riemannian products. Several examples are also given to illustrate the main concepts.
Keywords : Null hypersurfaces, isoparametric hypersurfaces, geodesics
MSC numbers : Primary 53C25, 53C40, 53C50
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