On the squares of umbilicity factors of null hypersurfaces in indefinite Kaehler manifolds
Acta mathematica Universitatis Comenianae, Tome 90 (2021) no. 1, pp. 99-110
Samuel Ssekajja; Samuel Ssekajja. On the squares of umbilicity factors of null hypersurfaces in indefinite Kaehler manifolds. Acta mathematica Universitatis Comenianae, Tome 90 (2021) no. 1, pp. 99-110. http://geodesic.mathdoc.fr/item/AMUC_2021_90_1_a6/
@article{AMUC_2021_90_1_a6,
     author = {Samuel Ssekajja and Samuel Ssekajja},
     title = { On the squares of umbilicity factors of null hypersurfaces in indefinite {Kaehler} manifolds},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {99--110},
     year = {2021},
     volume = {90},
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     url = {http://geodesic.mathdoc.fr/item/AMUC_2021_90_1_a6/}
}
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Any null hypersurface (M,g) of an indefinite Kaehler manifold, denoted as (\overline{M},\overline{g},\overline{J}), is endowed with two special null vector fields U:=-\overline{J}N and V:=-\overline{J}\xi, where N and \xi, respectively, span the transversal and normal bundle (radical distribution) to M. In this paper, we define the U and V-null sectional curvatures, and then apply them to totally umbilic null hypersurfaces. In particular, we prove that the squares of the umbilicity factors measures, up to third order, the differences in lengths of any two spacelike geodesics tangent to the \overline{J}-invariant distribution D_{0} over M.