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On transversely flat conformal foliations with good measures. II. (English) Zbl 0932.53023
The author uses a metric constructed by J. Ferrand [Math. Ann. 304, 277-291 (1996; Zbl 0866.53027)] to improve his previous results from Part I of this paper [T. Asuke, Trans. Am. Math. Soc. 348, 1939-1958 (1996; Zbl 0864.53019)]. Namely, he shows that foliations of closed manifolds which have transversely flat conformal structures and admit non-atomic, full support transverse invariant measures are Riemannian in the usual $$C^{\infty}$$-sense [see P. Molino, ‘Riemannian foliations’ (Progr. in Math. 73, Birkhäuser, Basel) (1988; Zbl 0633.53001)].

##### MSC:
 53C12 Foliations (differential geometric aspects)