M N (c) is parallel: Let X c T M and extend X along the r s p geodesic exp(tX) of M by p a r a l l e l t r a n s l a t i o n in TM . Xa) (X,X) = -(Vx~)(x,x) = 0 , so by the Codazzi e q u a t i o n V a = 0 and f is parallel. The r e m a i n d e r of this section is devoted to proving the other statements of T h e o r e m I, following the m e t h o d of StrHbing in [12]. We first d e v e l o p a F r e n e t theory for curves in a p s e u d o - R i e m a n n i a n m a n i f o l d and then use this to c o m p l e t e the proof of the theorem.