Sentence examples for be a closed null from inspiring English sources

Let ((M^{n+1},g,N)) be a closed null hypersurface of ((n+2))-dimensional (n>2) Lorentzian manifold ((overline{M},overline{g})) with (tau^{N}(xi)= 0), (N-xi) be a proper conformal Killing field with conformal factor 2λ, (lambda= frac {1}{n+2}operatorname{div}^{overline{g}} N-xi)).

Let ((M, g, N )) be a closed normalized null hypersurface with rigged vector field ξ.

Let ((M^{n+1},g,N)) be a closed normalized null hypersurface in a Lorentzian ((n+2))-manifold ((overline{M},overline{g})), (N-xi) be a proper conformal Killing field.

Let ((M,g,N) ) be a closed normalized null hypersurface with rigged ξ and (tau^{N}(xi) = 0 ) in a Lorentzian manifold.

Let ((M, g, N )) be a closed normalized null hypersurface with rigged vector field ξ and (tau^{N} (xi) = 0 ) in a pseudo-Riemannian manifold.

Let ((M,g,N )) be a closed normalized null hypersurface in a ((n+2))-dimensional Lorentzian manifold ((overline{M},overline{g})), (N-xi) be a proper conformally Killing field with conformal factor 2λ and (lambda=frac {1}{n+2}operatorname{div}^{overline{g}} N-xi)).

Let ((M^{n+1},g,N)) be a closed normalized null hypersurface in Lorentzian manifold ((overline{M},overline{g})), ((N-xi)) be a proper conformal Killing with conformal factor 2λ and (lambda= frac{1}{n+2}operatorname{div}^{overline{g}} N-xi)) and (tau^{N} N-xi0).

Let ((M, g,N )) be a closed normalized null hypersurface in ((n+2))-dimensional Lorentzian manifold ((overline{M},overline{g})), (N-xi) be a proper conformal Killing field with conformal factor 2λ and (lambda= frac{1}{n+2}operatorname{div}^{overline{g}} N-xi)).

Let ((M,g,N )) be a closed normalized null hypersurface in a ((n+2))-dimensional Lorentzian manifold ((overline{M},overline{g})) with constant sectional curvature k, ((N-xi)) be a proper conformal Killing field with conformal factor 2λ and (lambda= frac{1}{n+2}operatorname{div}^{overline{g}} N-xi)).

We shall give the following result, involving the extrinsic Ricci curvature Ric to the associated Ricci curvature (operatorname{Ric}^{eta}). Let ((M,g,N)) be a closed normalized null hypersurface with rigged vector field ξ and (tau^{N} (xi =0 ) in a ((n + 2 -pseudo-Riemannian manifold.

Let ((M^{n+1},g,N)) be a closed normalized and conformal screen null hypersurface in a Lorentzian ((n+2))-manifold ((overline{M},overline{g})) with conformal factor (varphi=1) and (N-xi) be a proper conformal Killing field.