projective vector造句

• Several important special cases of projective vector fields can occur and they form Lie subalgebras of P ( M ).
• The set of all global projective vector fields over a connected or compact manifold forms a finite-dimensional Lie algebra denoted by P ( M ) ( the "'projective algebra "') and satisfies for connected manifolds the condition : \ dim P ( M ) \ le n ( n + 2 ).
• Here a projective vector field is uniquely determined by specifying the values of X, \ nabla X and \ nabla \ nabla X ( equivalently, specifying X, h, F and \ psi ) at any point of M . ( For non-connected manifolds you need to specify these 3 in one point per connected component . ) Projectives also satisfy the properties:
• Therefore, any given particle is associated with a unique ( possibly trivial ) representation of " G " on a projective vector space "'P "'H . ( We say the particle " lies in ", or " transforms as " the representation . ) In many important cases, it can be shown that the particle is also ( more specifically ) associated with a group representation of " G " on the underlying ( non-projective ) space H.