L. ?-x-l-+-x-=-g(x,

, Lemma 4.15 The vector field L is geodesic, the distribution L ? is integrable and its integral manifolds are spherical

X. ?-l-l-=-?l-+-g(l,-l)l-=-field-;-l-?-.-if and Y. , Let us prove the integrability of

?. =-?-g(y,

Y. , X. )-?-g(x, Y. , [. , and Y. , This proves that L ? is involutive and hence integrable. Let O be an integral manifold of L ? . If X, Y ? VF(O)

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