Tautly foliated 3-manifolds with no R-covered foliations
نویسنده
چکیده
We provide a family of examples of graph manifolds which admit taut foliations, but no R-covered foliations. We also show that, with very few exceptions, R-covered foliations are taut.
منابع مشابه
Harmonic functions on R-covered foliations
Let (M,F) be a compact codimension one foliated manifold whose leaves are endowed with Riemannian metrics and consider continuous functions on M that are harmonic along the leaves of F . If every such function is constant on leaves we say that (M,F) has the Liouville property. Our main result is that codimension-one foliated bundles over compact negatively curved manifolds satisfy the Liouville...
متن کاملHarmonic functions on R-covered foliations and group actions on the circle
Let (M,F) be a compact codimension-one foliated manifold whose leaves are equipped with Riemannian metrics, and consider continuous functions on M that are harmonic along the leaves of F . If every such function is constant on leaves we say that (M,F) has the Liouville property. Our main result is that codimension-one foliated bundles over compact negatively curved manifolds satisfy the Liouvil...
متن کاملAdiabatic Limits and Foliations
We use adiabatic limits to study foliated manifolds. The Bott connection naturally shows up as the adiabatic limit of Levi-Civita connections. As an application, we then construct certain natural elliptic operators associated to the foliation and present a direct geometric proof of a vanshing theorem of Connes[Co], which extends the Lichnerowicz vanishing theorem [L] to foliated manifolds with ...
متن کاملEgorov’s theorem for transversally elliptic operators on foliated manifolds and noncommutative geodesic flow
The main result of the paper is Egorov’s theorem for transversally elliptic operators on compact foliated manifolds. This theorem is applied to describe the noncommutative geodesic flow in noncommutative geometry of Riemannian foliations.
متن کاملOn Elliptic Genera and Foliations
We prove several vanishing theorems for a class of generalized elliptic genera on foliated manifolds, by using classical equivariant index theory. The main techniques are the use of the Jacobi theta-functions and the construction of a new class of elliptic operators associated to foliations.
متن کامل