Sentence examples for be a null rigging from inspiring English sources
Let ((M,g)) be a null hypersurface of a Lorentzian manifold ((overline {M}^{n+2},overline{g})), ((overline{M}, overline{g}_{eta} )) be a Riemannian manifold constructed from the ambient Lorentzian, N be a null rigging for M fixed on M̅ satisfying (8) and ξ be a rigged field of M.
Let N be a null rigging of a null hypersurface of a Lorentzian manifold ((overline{M}^{n+2},overline{g})) and θ the 1-form metrically equivalent to N defined on some open set containing M and given by theta=overline{g}(N,cdot). (10) Suppose that eta= i^{star}{theta} (11) is a restriction to M, (i: Mrightarrowoverline{M} ) being the inclusion map.
From now on, we denote the normalized (or rigged) null hypersurface by a triplet ((M,g,N )) where (g = overline{g}_{|M}) is the first fundamental form and N is a null rigging for M.
A vector field N as defined in (8) is called a null rigging of M. It is noteworthy that the choice of a null transversal vector field N along M determines the null transversal vector bundle, the screen distribution and a unique radical vector field ξ, say the rigged vector field, satisfying (8).
Given a null hypersurface ((M,g)) in a Lorentzian manifold ((overline{M}^{n+2},overline{g})), first, we fix a null rigging N fixed on M̅, θ is an 1-form given by (10).
An outstanding property of a rigging is that it allows a definition of geometric objects globally on M. We say that we have a null rigging when the restriction of L to the null hypersurface is a null vector field.
Throughout the paper, we fix a null rigging N for M on M̅.
"It's a null trial," said Dr. David Felson, a rheumatologist at Boston University.
The gene pool of Deaf and gay individuals was a null set.
A striking fact is that the null rigging of the null hypersurface M is the normal unit vector field to the immersion of ((M,g_{eta})) into ((overline{M}, overline{g}_{eta})).
