Erratum to the paper “On quasi-Riemannian foliations”

✍ Scribed by Pawel G. Walczak

• Publisher: Springer
• Year: 1991
• Tongue: English
• Weight: 36 KB
• Volume: 9
• Category: Article
• ISSN: 0232-704X
• DOI: 10.1007/bf00136818

✦ Synopsis

The argument used in my paper does not work. Namely, the dimension of the space of horizontal vectors tangent to the bundle E considered in the paper is in general less than the dimension of the manifold M. So, the proof of Theorems 1 and 2 in Section 4 is not correct. However, using the estimates of the Lyapunov exponents of Lemma 2, Lemma 3, the Proposition of Section 3 and the Pesin's estimate of entropy [1] one can easily get the following:

Theorem. There exists an ij > 0 such that for any Riemannian manifold M offinite volume and negative sectional curvature KM _ -1 and any transversely complete harmonic (£, 2)-quasi Riemannian foliation F of M with e < the topological entropy h(tp) of the geodesic flow p = () of the orthogonal complement of Y is positive.

Corollary. If M is compact and KM < O, then the entropy of the geodesic flow of the orthogonal complement of any harmonic Riemannian foliation of M is positive.