Some integrations on null hypersurfaces in Lorentzian manifolds
Bull. Korean Math. Soc. 2019 Vol. 56, No. 1, 229-243
Published online 2019 Jan 31
Fortun\'{e} Massamba, Samuel Ssekajja
Private Bag X01, Scottsville 3209; Private Bag X01, Scottsville 3209
Abstract : We use the so-called pseudoinversion of degenerate metrics technique on foliated compact null hypersurface, $M^{n+1}$, in Lorentzian manifold $\overline{M}^{n+2}$, to derive an integral formula involving the $r$-th order mean curvatures of its foliations, $\mathcal{F}^{n}$. We apply our formula to minimal foliations, showing that, under certain geometric conditions, they are isomorphic to $n$-dimensional spheres. We also use the formula to deduce expressions for total mean curvatures of such foliations.
Keywords : null hypersurface, Newton transformation, foliation
MSC numbers : Primary 53C50; Secondary 53C12, 53C40
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