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- Title
Normalized null hypersurfaces in nonflat Lorentzian space forms satisfying L<sub>r</sub>x = Ux + b.
- Authors
FOTSING TETSING, Hans
- Abstract
In the present work, we classify normalized null hypersurfaces x : (M, g, N) → Q n+2 1 (c) immersed into one of the two real standard nonflat Lorentzian space-forms and satisfying the equation Lrx = Ux + b for some field of screen constant matrices U and some field of screen constant vectors b ∈ R n+2, where Lr is the linearized operator of the (r + 1)−mean curvature of the normalized null hypersurface for r = 0, ..., n. We show that if the immersion x is a solution of the equation Lrx = Ux + b for 1 ≤ r ≤ n and the normalization N is quasi-conformal, then M is either an (r + 1)−maximal null hypersurface, or a totally umbilical (or geodesic) null hypersurface or an almost isoparametric normalized null hypersurface with at most two non-zero principal curvatures. We also show that a null hypersurface M, of a real standard semi-Riemannian nonflat space form Q n+2 t (c), admits a totally umbilical screen distribution (and then M is totally umbilical or totally geodesic) if and only if M is a section of Q n+2 t (c) by a hyperplane of R n+3 . In particular a null hypersurface M → Q n+2 t (c) is totally geodesic if and only if M is a section of Q n+2 t (c) by a hyperplane of R n+3 passing through the origin.
- Subjects
HYPERSURFACES; USER experience; IMMERSIONS (Mathematics); CURVATURE; GEODESICS; DIFFERENTIAL operators; EQUATIONS
- Publication
Turkish Journal of Mathematics, 2021, Vol 45, Issue 4, p1809
- ISSN
1300-0098
- Publication type
Article
- DOI
10.3906/mat-2102-37