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Unformatted text preview: . Thus d dt ( f t ) t = = X ( f ) . Let Y be another vector eld on M . Then d dt Y (( f t )) t = = Y ( X ( f )) . Then at the point t ( x ) we have two di erent well dened vectors, Y t ( x ) and t * Y x . Diagram. Denition 5.1.1 A vector eld Y is invariant under the ow t gener-ated by a vector eld X if Y t ( x ) = t * Y x . An invariant vector eld Y is also called a Jacobi eld . di geom.tex; April 12, 2006; 17:59; p. 108...
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