Some integrations on null hypersurfaces in Lorentzian manifolds
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초록
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.
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.
참고문헌 (15)
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