Vector Fields on Complex and Real Manifolds
S. Bochner · Annals of Mathematics · 1950
vanishes identically, then there exists on V2k no analytic vector field Xa or tensor field a l' a other than zero. In this statement, covariant and contravariant may be interchanged. PROOF. If for a vector na we form the system (3) then, by our hypothesis, the constants c' in it must all vanish. However our assumption also implies that the rank of the k by k + 1 matrix (2) must at some point have its maximal value k, and an analytic solution ia of the system