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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.
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참고문헌 (24)
참고문헌 신청
L. J. Alas / 2004 / Hypersurfaces with constant mean curvature and two principal curvatures in Sn+1 / An. Acad. Brasil. Cienc. 76(3):489~497
C. Atindogbe / 2009 / Scalar curvature on lightlike hypersurfaces / Applied Sciences 11:9~18
C. Atindogbe / 2003 / Pseudoinversion of degenerate metrics / Int. J. Math. Math. Sci 2003(55):3479~3501
C. Atindogbe / 2014 / Lightlike hypersurfaces in Lorentzian manifolds with constant screen principal curvatures / Afr. Diaspora J. Math 16(2):31~45
J. Berndt / 1989 / Real hypersurfaces with constant principal curvatures in complex hyperbolic space / J. Reine Angew. Math 395:132~141
C. Atindogbe / 2009 / Scalar curvature on lightlike hypersurfaces / Applied Sciences 11:9~18
C. Atindogbe / 2003 / Pseudoinversion of degenerate metrics / Int. J. Math. Math. Sci 2003(55):3479~3501
C. Atindogbe / 2014 / Lightlike hypersurfaces in Lorentzian manifolds with constant screen principal curvatures / Afr. Diaspora J. Math 16(2):31~45
J. Berndt / 1989 / Real hypersurfaces with constant principal curvatures in complex hyperbolic space / J. Reine Angew. Math 395:132~141
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